Brett A. Bednarcyk

Glenn Research Center, Cleveland, Ohio

Phillip W. Yarrington, Ryan C. Lucking, Craig S. Collier, and James J. Ainsworth

Collier Research Corporation, Newport News, Virginia

Efficient Design and Analysis of Lightweight 

Reinforced Core Sandwich and PRSEUS Structures

NASA/TM—2011-217198

December 2011

AIAA–2011–1909
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientific and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Officer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major significant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of significant 

scientific and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientific 

and technical findings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientific and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientific, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
Brett A. Bednarcyk

Glenn Research Center, Cleveland, Ohio

Phillip W. Yarrington, Ryan C. Lucking, Craig S. Collier, and James J. Ainsworth

Collier Research Corporation, Newport News, Virginia

Efficient Design and Analysis of Lightweight 

Reinforced Core Sandwich and PRSEUS Structures

NASA/TM—2011-217198

December 2011

AIAA–2011–1909

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

52nd Structures, Structural Dynamics, and Materials Conference

cosponsored by the AIAA, ASME, ASCE, AHS, and ASC

Denver, Colorado, April 4–7, 2011
Acknowledgments

The authors would like to acknowledge the technical contributions of Elias Toubia of WebCore Technologies, Alex Velicky, Victor 

Li and Nicolette Yovanof of the Boeing Company, and Dawn Jegley at NASA Langley Research Center. Development of the 

Reinforced Core Sandwich concept was funded by NASA under the Advanced Composite Technology (ACT) Program, COTR 

Steven Arnold, NASA Glenn Research Center. Development of the PRSEUS contract was funded by The Boeing Company, 

Huntington Beach, California.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identification 

only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-217198 1

Efficient Design and Analysis of Lightweight 

Reinforced Core Sandwich and PRSEUS Structures

Brett A. Bednarcyk

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Phillip W. Yarrington, Ryan C. Lucking, Craig S. Collier, and James J. Ainsworth

Collier Research Corporation

Newport News, Virginia 23606 

Abstract

Design, analysis, and sizing methods for two novel structural panel concepts have been developed 

and incorporated into the HyperSizer Structural Sizing Software. Reinforced Core Sandwich (RCS) 

panels consist of a foam core with reinforcing composite webs connecting composite facesheets. Boeing’s 

Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) panels use a pultruded unidirectional 

composite rod to provide axial stiffness along with integrated transverse frames and stitching. Both of 

these structural concepts are oven-cured and have shown great promise for applications in lightweight 

structures, but have suffered from the lack of efficient sizing capabilities similar to those that exist for 

honeycomb sandwich, foam sandwich, hat stiffened, and other, more traditional concepts. Now, with 

accurate design methods for RCS and PRSEUS panels available in HyperSizer, these concepts can be 

traded and used in designs as is done with the more traditional structural concepts. The methods 

developed to enable sizing of RCS and PRSEUS are outlined, as are results showing the validity and 

utility of the methods. Applications include several large NASA heavy lift launch vehicle structures.

1.0 Introduction

The HyperSizer Structural Sizing Software (Ref. 1) is used extensively in industry and government 

(particularly NASA) to design lightweight composite structures. The software couples with a shell and 

beam-based finite element (FE) model of a structure to obtain the global loads associated with each load 

case. These loads are then statistically processed by HyperSizer to arrive at design-to loads for each 

individual panel (or beam) that comprise the structure. These individual user-specified regions, each with 

its own design-to load, are referred to as components. Users specify the type (or types) of panels or beams 

to be considered for each component, along with ranges of geometric variables (e.g., facesheet thickness, 

web height, etc.) and material options (e.g., ply materials and layups). The software then selects the 

lightest weight design permutation from all of the possible specified candidates that provides all positive 

margins for all load cases and all failure modes. Each panel and beam component has thus been sized and 

potentially changed, so the software writes new panel and beam definitions to the FE model. The FE 

model is then re-analyzed to allow the global loads to redistribute in response to the new design produced 

by HyperSizer. The new loads are then taken by HyperSizer to produce a new, updated design, and the 

process continues iteratively until convergence is achieved.

Key to the sizing process described above is the ability of HyperSizer to localize further the design-to 

loads for the panels and beams to the object and ply level, where many of the failure modes are operative.

For example, for a hat-stiffened panel, the panel level loads are first localized to the hat crown, web, and 

flange (as well as the facesheet open and closed span), which are referred to as objects. These object loads 

are then used to evaluate a particular design permutation versus local buckling failures. Further 

localization, to the level of the ply, enables evaluation of the design with respect to ply level failure 

criteria such as max stress, Tsai-Wu, and LaRC03. Only when a particular panel or beam design satisfies 

all failure modes (i.e., a positive margin of safety is calculated for all load cases) on all scales (including 
NASA/TM—2011-217198 2

buckling at the panel level) is the design considered viable. Clearly, to calculate the margin of safety

associated with each failure mode, accurate and efficient methods are needed not only localize the design 

to loads properly, but also to determine the failure load for a particular mode of failure. Such methods 

have now been developed and incorporated into HyperSizer for two new panel structural concepts; 

Reinforced Core Sandwich (RCS) (Refs. 2 and 3) and Boeing’s Pultruded Rod Stitched Efficient Unitized 

Structure (PRSEUS) (Ref. 4).

2.0 Reinforce Core Sandwich (RCS) Panels

RCS is a novel sandwich panel concept produced by WebCore Technologies(Refs. 2 and 3) that 

combines features of foam core sandwich panels and stiffened panels. Note that this structural concept in 

the past has been referred to as WebCore (Ref. 5) and Fiber Reinforced Foam (FRF) (Refs. 6 and 7), but 

the name Reinforced Core Sandwich has been adopted by HyperSizer. This type of panel is constructed 

by starting with long strips of closed-cell structural foam, such as Rohacell (Evonik Industries), with 

rectangular cross sections. These strips are wrapped with dry carbon fibers and placed adjacent to each 

other on a tool with dry carbon fiber facesheet preforms on the top and bottom. The panel is then 

infiltrated with resin via vacuum-assisted resin transfer molding (VARTM) (Ref. 8). Once the panel is 

infiltrated and cured, the fiber overwraps located between the foam strips form integral composite webs

(Figure 1). The webs provide significantly improved through-thickness shear strength compared to foam 

sandwich panels, while the foam provides support for the webs against local buckling. The webs also 

provide some axial strength and stiffness; however, this is not their primary purpose as they typically do 

not contain axial fibers, as the wrapping procedure requires a minimum helical angle of approximately 5°.

The facesheets provide most of the panel’s bending stiffness as they are located farther from the panel 

neutral axis. Biaxial RCS panels, with webs running in both directions can also be produced by cutting 

sticks from the dry core preform. However, in this case, only the webs running in one direction will be 

continuous.

Compared to aluminum honeycomb sandwich panels, RCS sandwich panels have the advantage of not 

requiring an adhesive between the facesheet and core, which adds parasitic mass, and debonding between 

facesheet and core is not typically an issue with RCS. Furthermore, RCS sandwich panels provide improved 

through-thickness shear strength in the web direction compared to aluminum honeycomb sandwich panels 

and they do not exhibit reduced shear strength as the panel thickness increases. Finally, the RCS sandwich 

concept is highly damage tolerant as its multiple webs, which are supported by the foam, provide redundant 

load paths, and, as stated above, the facesheets do not tend to delaminate from the core. The RCS preform 

can also be stitched prior to resin infiltration to further improve damage tolerance.

The primary application of the RCS concept to date has been in wind turbine blades, where the 

concept reduces cost and improves performance compared to balsa and PVC foam designs. Because cost 

is a primary driver in this application, glass fibers are typically used rather than carbon fibers. RCS is also

Figure 1.—(a) WebCore RCS panels with and without foam removed. (b) Typical RCS panel. (c) Large curved RCS 

panel infiltrated by Janicki.

(a) (b) (c)

1/16th Section 

of 33’ Barrel
NASA/TM—2011-217198 3

currently employed in marine structural applications, such as hulls, decks, bulk-heads, cockpit floors, hard 

tops, and fishing tower platforms. Additional non-aerospace applications include specialty shelters, high 

impact matting, and bridge decks. Aerospace applications for RCS include the ATK shroud boat tail 

demonstration article (Ref. 8), an impact-resistant turbine fan case designed and fabricated with NASA 

Glenn Research Center, and a weapons bay door for a Boeing UCAV, all of which were designed and 

manufactured using carbon fibers. In addition, preliminary designs of the NASA Crew Exploration 

Vehicle Crew Module (Ref. 5), the NASA Ares V shroud (Ref. 7), and the NASA Ares V interstage and 

intertank (Ref. 6) were reported using the RCS concept.

3.0 Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) Panels

The PRSEUS concept has been developed by Boeing as part of a decade long effort to bring stitched 

composite components into production (Refs. 4 and 9). As shown in Figure 2, PRSEUS features precured 

unidirectional composite rods at the top of the stringers that provides significant axial stiffness.

Transverse foam core sandwich frames provide stability to the stringers, which are accommodated with a 

pass through slot. The PRSEUS dry preform is assembled and stitched prior to resin infusion and oven 

curing. Stitching provides PRSEUS with a high level of damage tolerance as the stringers and frames do 

not delaminate from the facesheet and facesheet cracks tend to be deflected (Ref. 4). Example PRSEUS 

panels are shown in Figure 3.

Inclusion of this panel concept into HyperSizer presents several unique design features with respect to 

other panel types. First, this concept includes integrated transverse frames rather than relying on 

traditional skin stringer design with ring-frame beams. This allows the panel to efficiently handle biaxial 

loads, however, it makes this a challenging concept to optimize because the stringers and frames must be 

optimized simultaneously to obtain the lightest, most efficient structure. Second, this panel concept 

includes a very stiff pultruded rod stringer rather than a traditional flange. Early on, we recognized 

stability of this rod as an analysis challenge requiring a stiffener failure method not in present versions of 

HyperSizer. Finally, this panel concept, as opposed to more traditional designs has the ability to operate 

well into the postbuckling regime, and an analysis technique for robustly analyzing into this regime was 

needed so that PRSEUS panels could be efficiently sized to include postbuckling.

Figure 2.—Schematic of the PRSEUS structural concept.
NASA/TM—2011-217198 4

Figure 3.—Example PRSEUS panels.

4.0 Design and Analysis Methods

4.1 Reinforced Core Sandwich (RCS) Panels

RCS panels are similar to honeycomb and foam sandwich panels in that the primary function of the 

core is to separate the facesheets to increase the bending stiffness and to provide through-thickness 

strength and stiffness. In honeycomb and foam sandwich panels, it is typically assumed that the core does 

not contribute to the panel in-plane stiffness and strength. In the case of RCS, the composite material 

formed by the wrap layers does provide some contribution to the panel properties in the web direction 

(similar to a blade-stiffened sandwich panel). The variables associated with the design of an RCS panel 

include top facesheet thickness and material, the bottom facesheet thickness and material, the web 

thickness and material, the web spacing, the panel height, and the foam material (see Figure 4). The 

implementation of the concept in HyperSizer automatically adds half of the web material or layup to the 

top facesheet and half to the bottom facesheet to properly account for the wrap fibers, forming top and 

bottom face “combos”. Once the wrap layers are correctly combined with the top and bottom facesheets, 

HyperSizer determines the effective ABD stiffness terms of the RCS panel identically to the methods 

used for a blade-stiffened sandwich panel. That is, the contribution of the foam to the panel stiffness is 

ignored. The foam does, however, play an important role in the failure methods for RCS.

Table 1 summarized the failure modes observed for RCS panels and details of the method 

implemented to capture the mode. For composite strength, standard failure criteria are used at the ply 

level once ply level stresses and strains have been determined. To obtain these ply level stresses, it is

Figure 4.—Schematic of and RCS panel cross-section showing composition and design variables.

z

y
NASA/TM—2011-217198 5

assumed that the panel loads Ny, Nxy, My, and Mxy are reacted by the facesheet combos only, whereas, 

Nx, Mx, are reacted by the facesheet combos and the webs. Qy is reacted only by the foam. Qx is reacted 

by the foam and the webs, but due to orientation of the web, Qx enters as a local Nxy. The panel Qx is 

distributed to the foam and the web based on their relative stiffness and area. For shear failure of the 

foam, the Qx and Qy reacted by the foam are divided by the thickness to obtain the through-thickness 

shear stresses in the foam. These are directly compared to the allowables and also combined in a quadratic 

interaction criterion. If the panel is subjected to pressure, a through-thickness compressive stress is 

calculated for the foam based on distributing the pressure to the webs and the foam (again, based on their 

relative stiffnesses and areas) and compared to the foam crush allowable. For shear crimping, which is a 

short wave buckling mode caused by low core through-thickness shear stiffness (Ref. 1), the effective 

through-thickness shear stiffness of the core was calculated via a Voigt relation,

1 foam

eff w w w xz xy

x x

t t GG G

S S

 

= +−     (1) 

where tw is the web thickness, Sx is the stiffener spacing, w Gxy is the web effective in-plane shear modulus, 

and Gfoam is the shear modulus of the foam. This effective core shear stiffness is used in the shear 

crimping allowable equation in the web direction (x-direction), whereas, in the y-direction, the foam shear 

stiffness is used. The effective shear stiffness of the core is also used in the HyperSizer panel buckling 

equations for RCS to calculate the transverse shear flexibility correction factor. For facesheet wrinkling, a 

similar Voigt-type equation is used to determine the effective core through-thickness crush stiffness for 

use in the sandwich facesheet wrinkling equations (Ref. 10).

TABLE 1.—BRIEF DESCRIPTION OF RCS PANEL FAILURE MODES 

AND ASSOCIATED METHODS IMPLEMENTED WITHIN HyperSizer

Mode Objects(s) Description/method 

Composite 

strength Web, facesheet 

• Based on loads (N, M, Q) on panel

• Web acts as decoupled, but panel Q goes into web as web Nxy 

• Foam assumed to only affect the Nxy in the web

• Many standard failure criteria (max stress/strain, Tsai-Wu, Hashin, LaRC03, etc.) 

• Added localization to get Q distribution between web and foam 

Shear strength Foam 

• Due to through-thickness shears on panel Qx, Qy 

• Compare shear stress in foam to allowable

• Check Qx, Qy, quadratic interaction

• Added localization to get shear stress in foam 

Crushing Core 

• Due to pressure crushing panel, through-thickness shear loads crushing core against 

a flange

• Resulting stress, localized to foam, compared to core crush allowable

• Added localization of crush stress to foam 

Shear crimping Core 

• Short wave buckling of panel due to low core stiffness 

• Based on through-thickness shear moduli of core, no interaction 

• Added homogenization of web/foam to get effective shear stiffness of core 

Panel buckling Panel 

• Based on panel-level ABD and panel through-thickness shear stiffness

• Foam assumed to only affect through-thickness shear stiffness 

• Added homogenization of web/foam to get effective shear stiffness of core 

Wrinkling Facesheet 

• Local shortwave buckling of facesheet

• Classical method for sandwich panels 

• Added homogenization of web/foam to get effective crush stiffness of core 

Local buckling Web, facesheet 

• Standard HyperSizer method treats web and FS as plate with simple support on all 

edges

• Does not include support provided by foam between webs and facesheets

• Added new method to HyperSizer based on buckling on elastic foundation models 
NASA/TM—2011-217198 6

For local buckling of the RCS web and facesheets, significant effort was required to develop viable 

methods for use in HyperSizer. This is because the main benefit of the foam material is to provide support 

for the web and facesheet against buckling. Thus this support must be accounted for in the HyperSizer 

methods to size RCS panels that are truly optimized. As such, the standard approach to local buckling of 

stiffened panels in HyperSizer were used, wherein the web and facesheets are treated as simply supported 

plates and the moments and coupling stiffness terms are ignored, with the addition of support provided by 

the foam. A Winkler (spring-like) foundation model, where a linear relation is assumed between the plate 

deflection and the pressure exerted by the foundation on the plate has been implemented. The standard 

anisotropic plate bending equation, with coupling stiffness terms assumed to be zero (Ref. 11), can then 

be written as, 

( )

x y

w N

y

w N

x

w Kw N

x

w D

y x

w D

x y

w D D

x y

w D

x

w D

x y xy ∂ ∂

∂

+

∂

∂

+

∂

∂

+ = ∂

∂

+

∂ ∂

∂

+

∂ ∂

∂

+ +

∂ ∂

∂

+

∂

∂

2

2

2

2

2

4

4

22

3

4

26 2 2

4

12 66 3

4

16 4

4

11

2

4 2 2 4

(2) 

where the pressure has been written as a stiffness K of the foundation (also known as the bedding 

constant) times the plate deflection, w. We consider the section of facesheet between the webs, or the 

webs themselves, to be infinite strips in shear as they are much longer in the web direction than between 

the webs. In compression, a finite plate is considered. To further simplify the problem, shear loading and 

a single compressive normal load component are considered as separate cases. 

For an infinite strip subjected to shear loading, Nxy = t, as shown in Figure 5 under simply supported 

boundary conditions, Timoshenko’s (Ref. 12) method is used where it is assumed that the buckled plate 

deflection is given by,

(x y) b s

y w A απ π = sin sin − (3) 

where A is a constant, b is the width of the strip, s is the x-distance between buckling half-waves, and α is 

slope in x-y coordinates of the buckling wave nodes. The terms s and α must be determined. This 

deflection is shown in Figure 6.

To determine the approximate critical buckling load, the principal of minimum potential energy,

∂Π = ∂ + (U V ) (4) 

is used, where the strain energy due to bending is given by,

( ) ( )( ) ( )

( ) ( )

2 2

1 11 , 12 , , 22 ,

2

16 , 26 , , 66 ,

1 2

2

4 4

xx xx yy yy

xx yy xy xy

U Dw Dw w D w

D w D w w D w dx dy

 =+ + 

 ++ + 

∫∫

(5)

the strain energy due to the deformation of the elastic foundation is given by,

(6) 2

2

1

2 U Kw dxdy = ∫∫
NASA/TM—2011-217198 7

Figure 5.—Infinite strip used to model the webs or facesheet located between webs 

subjected to shear loading.

Figure 6.—Assumed buckled mode shape for infinite strip 

under simple support subjected to shear loading.

and the work done by the loads is given by,

V [ Nx (W,xx ) Ny (W, yy ) 2Nxy (w,x )(w, y )] dxdy 2

1 2 2

= + + ∫∫ (7)

The deflection, Equation (3), is substituted into Equations (5), (6), and (7), which are integrated over the 

area of a buckling half-wave (y = 0, b; x = 0, s). The variation of the total potential energy, Equation (4), 

is minimized by setting the second derivative of U1 + U2 + V with respect to A to zero. This can be solved 

for the critical shear buckling load, tcr, 

b

x

y

Simply supported

Simply supported

α
NASA/TM—2011-217198 8

α

π α α α α

α

π α α

α

π

4

11 16 12 66 26 22

4 4

22

4

4

26 22

2 2

2

2

12 66

( ) ( ( 4 (2 4 ( 4 ))))

( 2 ) 3 ( 2 )

b

b K D b D D D D D D

b

b D D

b

D D

tcr

− − − + − + + + − +

+

− +

+

+ =

(8)

where an expression for the variable, s, has been determined by minimizing tcr with respect to this 

variable. Equation (8) still contains the variable α, which is determined by numerically minimizing tcr

with respect to this variable.

For compressive loading, a finite plate simply supported on all edges is considered (Figure 7). The 

assumed form of the buckled deflection that satisfies Equation (2) is,





 





















= b

y sin

n

a

 x sin π π

w A (9) 

(see Figure 8) where n is the number of buckling half-waves in the x-direction. Following a similar 

procedure to that used in the case of shear loading, the critical normal buckling load can be determined as,

( ( ))

( )

2 2 24 4 44 4 4 4

12 66 11 22

242 2

2 2 ( 2)

2 cr

n ab D D n bD n a bK D

P

abn n

− + + ++

=

π ππ π

π π

(10) 

In HyperSizer, the critical Nxy load for the RCS facesheet and web is determined from Equation (8), 

while the critical Nx and Ny loads are determined individually from Equation (10). Then, to determine 

failure under combined loads, the following interaction equation is used,

1

2 2 2

= 















+ 















+ 















cr

xy

xy

cr

y

y

cr

x

x

N

N

N

N

N

N (11) 

where the superscript cr denotes a critical load, and the load terms without superscripts are the web or 

facesheet loads determined by HyperSizer.

To evaluate Equations (8) and (11), a value for the foundation stiffness, or bedding constant (K) is 

needed. Two methods for determining the value of K have been implemented in HyperSizer. The 

effective stiffness approach is based on the modulus and width of the foam. For the web, with two-sided 

support by the foam (Figure 4), the effective stiffness is given by (Ref. 13),

K = Efoam hcore (12) 

and for the facesheet, with one-sided support,

( ) K = Efoam 2Sx (13) 

The second approach was suggested by Hetenyi (Ref. 13), with the value for the web given by,

( ) 



 



 = 3

1

web

foam foam 11 K 2 0.28E E D (14) 

and for the facesheet,

( )3

1

foam foam 11 0.28 K E E DFS = (15) 
NASA/TM—2011-217198 9

Figure 7.—Finite plate used to model buckling of 

RCS webs and facesheets under normal loading.

Figure 8.—Assumed buckling mode shape for finite

simply supported plate under uniaxial compressive 

load.

4.2 Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) Panels

The analysis methods specific to PRSEUS fall within two major categories. The first is thermoelastic 

formulation of the entire panel 3D cross-section into a 2D planar equivalent representation quantified with 

fully coupled terms in the 6x6 matrix. This part of the analysis doesn’t receive as much fanfare as does 

the other aspect which is failure prediction. However, accurate failure prediction could not take place 

without accurately representing the elastic response of the panel to any general loading condition.

The second general category of analysis is failure prediction. HyperSizer already had many of the 

failure methods needed to analyze the PRSEUS panel, however, two types of failure were identified as 

missing for PRSEUS panel analysis, these were local postbuckling of the facesheet and torsional buckling 

of the panel stiffener. The latter of these is especially important to predict stability of the stiffening rod. 

Analysis methods accounting for these failure methods were developed and verified against FEA as part 

of the PRSEUS panel development.
NASA/TM—2011-217198 10

Figure 9.—Schematic of the HyperSizer generating an equivalent panel stiffness from a 

candidate panel design.

4.2.1 Thermoelastic Formulation

The first step in characterizing any HyperSizer panel concept is in formulating the strain response of a 

panel to an applied load or thermal environment. All HyperSizer failure analysis is built on this 

foundation. HyperSizer analyzes stiffened panels composed of arbitrary composite laminates through 

stiffener homogenization, or “smearing”. The result is an effective constitutive equation for the stiffened 

panel that is suitable for use in a full vehicle-scale finite element analysis. The thermoelastic formulation 

of the PRSEUS panel extends existing methods for all other panel types.

As shown in Figure 9, for a give candidate panel design, HyperSizer generates a panel-level stiffness 

(constitutive equation). With this stiffness, HyperSizer applies the panel loads (Nx, Ny, Mx, etc.) to get the 

panel strains. With the panel strains, HyperSizer reverses the smearing process to back out the loads in 

each object.

The smearing process is done by extending classical lamination theory (CLT) to stiffened panels. The 

thermoelastic formulation of a panel takes on the form:

T

T

       = −                

N AB ε N

M BD κ M

(16) 

where N and M are the panel level forces, ε and κ are the panel level strains and curvatures respectively 

and NT and MT are the panel level thermal forces and moments. The ABD matrix is the classical panelstiffness matrix from CLT relating panel resultant forces and moments to strains and curvatures. The 

same assumptions used in CLT apply to the HyperSizer formulation. These are sometimes referred to as 

the Kirchhoff assumptions with the major assumption being that plane sections remain plane after 

bending. HyperSizer’s general thermoelastic formulations for representing stiffened panels as an effective 

ABD representation has been presented in some detail in previous papers (Refs. 14 and 15).

The overall ABD matrix for the panel can be derived by determining the A, B and D contributions of 

each constituent at the reference plane of the panel and simply adding these contributions. In other words,

A A AA A panel /Flange Rod Stringer Frame = ++ + FS

B B BB B panel /Flange Rod Stringer Frame = ++ + FS

D D DD D panel /Flange Rod Stringer Frame = ++ + FS

(17) 

Several extensions to HyperSizer’s methods were required to extend the HyperSizer panel 

formulation to the PRSEUS Panel concept. These extensions included the stiffness contributions of the 

flange and facesheet overlaps of both the stringers and frames, and the stiffness contribution of the 

unidirectional rod.
NASA/TM—2011-217198 11

4.2.2 Stiffness Contribution of the Flange and Facesheet Overlaps

The complete derivation of the stiffness contribution of the flange and facesheet overlap is beyond the 

scope of this paper; however the assumptions that go into this derivation are as follows. The flange and 

facesheet contribution to the overall stiffness of the panel is determined by combining the flange and 

facesheet into a single smeared stiffness. The equivalent, generalized stiffness terms are used to compute 

the average panel response, in terms of strains (εi) and curvatures (κi). From these average values 

identified at the panel’s reference plane, the strains and curvatures of each individual analysis object can 

be determined. This approach is straightforward for panel response in the longitudinal direction where the 

stiffener is continuous. However, in the transverse direction (perpendicular to the stiffener) the stiffness is 

discontinuous, as it changes abruptly from only the skin, to the combined skin and flange. Consider the 

panel shown Figure 10(a) and the corresponding response to transverse loading (Figure 10(b)). In 

HyperSizer, the panel is formulated by identifying regions or “segments”, determining the ABD matrix 

for each segment and then combining these segments to form effective ABD matrices for the overall 

panel. In the case of the PRSEUS stringer flange/facesheet, three segments are defined. Segment 1 is the 

open span facesheet laminate, Segment 6 is the combination of the facesheet and flange, and Segment 8 is 

the combination of facesheet/flange with the open span.

It is incorrect to assume that the average panel strain and the strain of the local objects are the same, 

meaning the object forces must be different.

[1] [6] [8] Wrong! εεε yyy = = ⇒

[1] [6] [8] Wrong! NN N y y ≠≠ ⇒ (18) 

However, the load path from one edge of the panel to the other edge of the panel must go through both the 

[1] and [6] objects. The HyperSizer formulation resolves this consistently by satisfying the object loads 

such that

[1] [6] [8] Correct! NN N yy y = = ⇒

[1] [6] [8] Correct! εεε yy y ≠≠ ⇒ (19) 

Figure 10.—(a) Definition of segments in a PRSEUS panel. (b) Deformation in response to transverse 

compression loading.

Ny

Neutral Axis = 

Reference Plane 

(for symmetric 

laminates)

Neutral Axis 

Shift ≠ 

Reference 

Plane

Seg[1] Seg[6] Seg[8] (a)

(b)
NASA/TM—2011-217198 12

Figure 11.—Depiction of iso-strain conditions for a 

layered panel segment.

Figure 12.—Definition of segment 9 for a PRSEUS panel.

In the x direction (along the stiffener), the assumption is that entire panel strains as a unit (iso-strain), 

see Figure 11, which gives:

εεε xx x [1] [6] [8] = =

NNN xxx [8] [1] [6] ≠ ≠ (20) 

For the PRSEUS panel, a facesheet/flange segment exists not only for the stringer flange, but also for 

the frame flange object. We call this combination “Segment 9”, see Figure 12. In this case, we formulate 

the combination object in exactly the same way except that in this case we assume iso-strain in the y 

direction, rather than in the x direction.

Therefore, we have the following assumptions:

[1] [7] [9] Correct! NN N xx x = = ⇒

[1] [6] [9] Correct! εεε xx x ≠≠ ⇒ (21) 

These assumptions for the stringers and flanges lead to a smeared equivalent ABD matrix which 

consistently represents the entire facesheet along with both the stringer and frame flange combos.

x

Seg [7] Seg [1] Seg [9]

Frame Span

= w[1] + w[7]

x

Nx[6]

Nx[1]

εx[1] = εx[6]
NASA/TM—2011-217198 13

4.2.3 Stiffness Contribution of the Stiffening Rod

The stiffening rod is an analysis object which is new to HyperSizer analysis, see Figure 13. The 

inclusion of a stiffening rod is a straightforward derivation assuming that the rods act only in the axial 

(i.e., x) direction. The expression for force in a single stiffening rod is simply a function of the area of the 

rod and the axial modulus of elasticity.

Axial F EA Rod Rod Rod =    ε (22) 

The force per unit length (Nx) exerted by all of the rods on the stiffened panel is the force on one rod 

divided by the stringer spacing, S.

Axial

Rod Rod

Rod

E A

N

S

  =      

ε (23) 

The term in brackets acts as an “A” membrane stiffness term. A similar expression can be found for 

the “D” bending contribution of the rod. The B membrane bending coupling of the rod is assumed to be 

zero. The contribution to the overall panel of the rods (in the reference plane of the rod) takes on the 

form:

Axial

0 Rod Rod

Rod

100

000

000

E A

S

 

  =  

   

A 0 B 0 Rod =

Axial

0 Rod Rod

Rod

100

000

000

yy E I

S

 

  =  

   

D (24) 

Figure 13.—PRSEUS panel stringer notation and dimensions.

Arod

hstringer
NASA/TM—2011-217198 14

Finally the contribution of the rod is transformed into the panel reference coordinate system using the 

parallel axis theorem so that it can be added to the overall panel ABD matrix.

0 A A Rod Rod = ( ) 0

Rod stringer Rod B A = h ( )

2 0 0

Rod Rod stringer Rod DD A = + h (25) 

4.2.4 Failure Analyses

The failure methods that have been identified as applicable to the PRSEUS concepts and are included 

in the HyperSizer PRSEUS panel analysis capability are described in Table 2.

TABLE 2.—BRIEF DESCRIPTION OF PRSEUS PANEL FAILURE MODES 

AND ASSOCIATED METHODS IMPLEMENTED WITHIN HyperSizer

Mode Component(s) Description/method 

Panel buckling Panel

• Based on panel-level smeared ABD Stiffness Matrix and panel Transverse 

Shear Flexibility (TSF)

• Numerical Raleigh Ritz and closed-form solutions for panel buckling of curved 

or flat panels in uniaxial, biaxial, and/or shear loading

Crippling Panel

• Based on loads on overall panel (N, M, Q)

• Semi-empirical method that uses load distribution in various objects such as 

facesheet, flanges, web

• Predicts overall panel collapse after local buckling of a portion of the panel 

concentrated in the remaining stable cross-section exceeds material ultimate 

strength

Johnson-Euler 

buckling-crippling 

interaction

Panel • This method combines the effects of panel buckling and crippling to predict 

ultimate failure load of the panel

Composite strength Web, facesheets

• Based on loads (N, M, Q) on panel

• Panel level Transverse Shear forces Qx, Qy goes into web and frames as inplane shear force, Nxy 

• Many standard failure criteria (max stress/strain, Tsai-Hill, Hoffman, etc.) 

Local buckling Web, facesheets

• Objects modeled as rectangular plates with simple support on all edges

• Fourier series solution of plate ODE, including Ny/Nx ratio 

• Shear buckling as a separate calculation - combined with biaxial buckling 

through quadratic interaction

• Many times this failure mode is not considered to be catastrophic

Local postbuckling Facesheets

• Redistributes load from buckled (ineffective) portion of panel to a calculated 

“effective” width.

• PRSEUS panel shown (both in analysis and test) to carry substantial 

postbuckling loads

• Predicts failure in postbuckling due to crippling, material strength, panel 

buckling

Torsional buckling Panel, stiffeners

• Failure of the panel due to “tipping” of the stiffener under compressive load.

Considered to be an ultimate failure.

• Calculates stability of stiffener by modeling the interface between stiffener and 

facesheet as a combination of linear and rotational spring constants

• Closed-form physics based method originally developed for metallic fastened 

panels extended to composite bonded panels including PRSEUS configuration

4.2.5 Instability Modes Applicable to PRSEUS

The general instability modes that are applicable to the PRSEUS Panel Concept and are included in 

the HyperSizer software are described in Table 3. 
NASA/TM—2011-217198 15

TABLE 3.—DETAILS OF PRSEUS INSTABILITY MODES

Panel Buckling Mode Comments Illustration

Initial instability

(skin buckling)

HyperSizer calculates local buckling of 

all panel objects. For the PRSEUS 

architecture, this will include :

a) the skin/flange region between both 

the stringer and frame stiffeners

b) the frame web and core

c) the stringer web

Flexural instability or panel 

buckling

(Euler mode)

HyperSizer includes methods for panel 

buckling of stiffened panels both for flat 

panels with simple boundary conditions 

and for curved panels with simple, fixed, 

or free BCs.

Torsional instability

This new failure method, developed in 

HyperSizer specifically for the PRSEUS 

panel concept captures torsional buckling 

of the stiffeners, also called tipping. It is 

thought that this is the most likely mode 

that could cause failure in the rod 

stiffeners themselves.

4.2.6 Local Buckling

The local buckling methods used by HyperSizer assume that panel objects behave like flat plates from 

a buckling perspective. HyperSizer uses closed-form methods to solve for local buckling of these objects 

so that the buckling solutions can be included in the full panel optimization process. 

There are three applicable local buckling objects in the PRSEUS panel concept.

1. Local buckling of the stringer web (Figure 14(a)). The assumption is made that the facesheet and 

stiffener rod act as perfect simple (or pinned) boundary conditions on the stringer web.

2. Local buckling of the frame web/foam (Figure 14(b)). These structures have a high bending 

stiffness due to their sandwich-like behavior, however they are generally spaced farther apart 

(i.e., 20 in. in the baseline panel) meaning that they will be more highly loaded in a panel biaxial 

loading scenario. In addition, these panels will be treated as having a “free” boundary, rather than 

having all edges simply supported. This will also adversely affect the buckling characteristics.

3. Local buckling of the “Spacing Span” (Figure 15). The spacing span is the region between the 

stiffeners which includes both the bare facesheet and the bonded flange regions. The assumption 

is that local buckling waves between stiffeners will not be restricted to just the facesheet, but will 

include the stiffeners as well. 

HyperSizer draws a distinction in the software between two objects called respectively “Open Span” 

and “Spacing Span”. The open span is the region of bare facesheet between the flanges of the stiffened 

panel. For stiffened panels with bonded stiffeners, unless the facesheets are extremely thin compared to 

the flanges, a local buckling wave will not occur in the open span, but rather in the spacing span, which is 

a region that goes from stiffener to stiffener. This is assumed to be the case for the PRSEUS panel 

concept. 
NASA/TM—2011-217198 16

Figure 14.—Local buckling objects for the PRSEUS panel: a) stringer web b) frame web and foam.

Figure 15.—Illustration of PRSEUS spacing span buckling.

Bare Facesheet

2 stacks, 14 plies

Overlap

7 Stacks, 49 plies

Stringer Bonded Flange, 

4 stacks, 28 plies

Frame Bonded Flange

5 stacks, 35 plies

20 in.

6 in.

Spacing Span

Open Span

Buckling wave travels through 

both facesheet and flange

(a)

(b)
NASA/TM—2011-217198 17

Figure 16.—A PRSEUS stiffened panel with a depicted local buckling mode shape.

4.2.7 Facesheet Postbuckling

The first failure mode for most stiffened panels (including PRSEUS) is usually initial buckling of the 

skin between stiffeners (Figure 16). After initial skin buckling, the stiffened panel can support additional

load. Allowing the skin to buckle at operational loads requires a local postbuckling analysis capability. 

As an example, consider the PRSEUS stiffened panel cross-section of Figure 17 loaded in uniform 

compression. At the onset of skin buckling (local buckling) the analysis is linear elastic, and all of panel 

objects such as the skin, stiffener web, and stiffener flange are loaded uniformly. The average level of 

stress is depicted as the horizontal dashed line in Figure 17(c). As additional load is applied to the panel, 

the buckled skin between stiffeners remains at the same stress (constant bifurcation load) and the 

additional load is picked up by the stiffener and the remaining effective width, be of the skin. As more 

load is applied, the effective width becomes more narrow and the remaining stable cross-section of skin 

and stringer carries higher load until either the material reaches compressive yield, the strip-column 

buckles, or the stiffener cripples. The actual state of stress distribution of Figure 17(d) is represented in 

the HyperSizer postbuckling method as a rectangular step function, as shown in Figure 17(e). For the 

PRSEUS panel, not only does the stringer cross-section continue to carry load in postbuckling, but the 

transverse frame cross-section carries additional load as well. 

Local postbuckling of a span is permissible if the panel can be shown to support additional load 

beyond the first occurrence of buckling (bifurcation point), without strength failure or collapse from 

buckling or cross-section crippling. In traditional metallic aerospace designs, the spans are allowed to 

local buckle even at limit loads, but normally not at loads below a prescribed level, such as 0.5 Design 

Limit Load (DLL). Postbuckling of composite structures are less common because of the possibility of 

stiffener debonding in the presence of buckling waves. However, PRSEUS’ inclusion of stitching 

between the facesheet and stringer flange enhances the bond strength making postbuckling more feasible 

than in traditional composite-stiffened designs. The local postbuckling method implemented in 

HyperSizer is discussed in more detail in References 16 and 17.

4.2.8 Torsional Buckling

An additional analysis method developed for the PRSEUS concept is torsional buckling of the 

stringer. This failure mode occurs when the stringer, which is stabilized by its connection to the facesheet, 

buckles out-of-plane, also known as stiffener “tipping.” This buckling mode in-turn reduces the bending 

stiffness of the overall panel. An antisymmetric torsional buckling mode for PRSEUS is shown in Figure 

18. 

Stiffener torsional buckling can be analyzed with finite element solvers. However, such analyses are 

computationally expensive and are not feasible options when rapid sizing of a stiffened panel is required. 

The number of iterations involved in optimization requires a rapid but accurate method. 
NASA/TM—2011-217198 18

Figure 17.—The effective width of the facesheet is included with the 

stiffener in the calculation of remaining panel stable cross-section. 

As load is increased the remaining effective width becomes 

narrower.
NASA/TM—2011-217198 19

Figure 18.—Illustration of torsional buckling of the stringers in a PRSEUS panel.

A closed-form method was developed by Argyris (Ref. 18) for metallic, single skin-stiffened panels. 

This method has been implemented and generalized in HyperSizer. Details of the method are not 

presented here but can be found in the HyperSizer documentation. Enhancements to the method include:

• General cross-sections (the original method only considered Z-type stringers)

• Bonded and riveted panels

• Composite materials

• Stiffening rods (rather than a free flange)

One feature of the PRSEUS concept that is not directly addressed by HyperSizer is the presence of 

stitching. Our understanding is that the purpose of the PRSEUS stitching is to increase the damage 

tolerance of the composite materials and to arrest cracks that might otherwise grow catastrophically in a 

more traditional composite. Our assumption is that stitching does not, however, affect the analysis 

methodology. Rather the effects of stitching are accounted for both in the composite modulus of elasticity 

and failure allowable material properties that are inputs to the HyperSizer analysis process. Therefore for 

purposes of calculating stability and failure methods in HyperSizer, no adjustment was made to account 

for stitching.

More importantly, stitching does affect the philosophy of assigning material allowables. With 

traditional composite design, the allowable strains can be “knocked down” more than 50 percent to 

account for Barely VIsible Damage (BVID) or Compression After Impact (CAI). A pristine coupon test 

with an average failure strain around 9000 μin./in. might be used in a design where the design-to strain 

allowable is below 4000 μin./in. to account for strength reduction due to BVID. In a stitched design, 

however, this practice might be overly conservative and higher design allowables might be used.
NASA/TM—2011-217198 20

Regardless, this is more of a design philosophy issue rather than an analysis or sizing issue addressed 

directly in HyperSizer.

5.0 Results and Discussion

5.1 Reinforced Core Sandwich (RCS) Panels

5.1.1 Verification/Validation Results

To verify the validity of the local buckling solution under shear loading, Equation (8), without the 

foundational support (i.e., K = 0), comparison is made to Saydel’s (Ref. 19) solution for [θ/–θ/θ/–θ] 

antisymmetric balanced angle-ply laminates. This class of laminates exhibits no normal-shear coupling 

(A16 = A26 = D16 = D26 = 0), but does have nonzero coupling stiffness terms, which are ignored by the 

Saydel (Ref. 19) solution and that presented above, Equation (8). The properties for the ply considered are 

given in Table 4. In Figure 19 the predicted critical shear buckling load is plotted versus the lamination 

angle for Saydel’s exact solution, finite element analysis (FEA) performed using Abaqus linear shell 

elements, and the present approximate solution, Equation (8). The FEA solution does include the effects 

of the coupling stiffness terms of the laminates. As Figure 19 shows, the present solution gives a good 

approximation of the exact and FEA solutions (without foundational support) with a very simple and 

efficient equation. The maximum difference of the present solution from the FEA is 6.5 percent.

Tests were also conducted to validate the local buckling solution for webs in RCS panels using 

specimens extracted from an RCS panel containing a single web like that shown in Figure 20. The 

predicted buckling loads from Equation (8), where the effective stiffness approach was used for K

(Eq. (12)) are compared with experimental results in Table 5. Clearly, the approximate solution matches 

quite well with the experimental data.

TABLE 4.—MECHANICAL PROPERTIES OF THE PLY CONSIDERED

FOR SHEAR BUCKLING OF AN UNSUPPORTED 

ANTISYMMETRIC ANGLE-PLY LAMINATE

Longitudinal modulus EL (GPa).........................................29.732

Transverse modulus ET (GPa)..............................................8.850

Shear modulus GLT (GPa)....................................................2.741

Poisson’s ratio νLT ...............................................................0.301

Figure 19.—Comparison of buckling load prediction for an unsupported antisymmetric angle-ply 

laminate by the present solution, the exact solution (Ref. 19), and FEA.
NASA/TM—2011-217198 21

Figure 20.—Shear specimen extracted from an RCS panel 

containing one web and adjacent foam.

TABLE 5.—COMPARISON OF PREDICTED AND EXPERIMENTAL

BUCKLING LOADS FOR SINGLE WEB RCS SPECIMENS

Specimen I.D. Experimental tcr

(lb/in.)

Predicted tcr

(lb/in.)

Error 

(%)

134-0304 226 240 6

76-62 314 264 15

For verification under normal compressive loading, comparison was made to Abaqus finite element 

solutions for facesheet buckling of an RCS panel. The panel geometry considered is shown in Figure 21.

The facesheets, denoted M1 and M5 in Figure 21, are both [02/45/–45/90/–452/45/03] layups, while the 

webs, denoted M3 in Figure 21, are [–45/45/–45/45] layups, with all plies having a thickness of 0.004167 

in. and the material properties given in Table 6. The foam material considered had a Young’s modulus of 

5.22 ksi and a shear modulus of 1.885 ksi. For the finite element model, linear shell elements were used 

for the facesheet combos and webs, while linear solid elements were used for the foam. An x-span of 

10 in. and a y-span of 7 in. were considered. S4R and C3D8I elements were used for the plate and solid 

elements, respectively. A mesh convergence study was performed to arrive at the mesh shown in Figure 

22, shown both with and without the foam material. Displacement boundary conditions were imposed, as 

shown in Figure 23, with two additional point constraints on z-displacement as shown. A biaxial load of 

Nx = –4520 lb/in. and Ny = 495 lb/in. was imposed by applying the correct displacements that resulted in 

these loads. Table 7 shows a comparison of the object loads predicted by HyperSizer and FEA for the 

panel. These loads are in excellent agreement.

TABLE 6.—MATERIAL PROPERTIES FOR PLIES IN RCS

PANELS SUBJECTED TO NORMAL LOADING

Longitudinal modulus EL (Msi) .............................................21.2

Transverse modulus ET (Msi) ................................................1.82

Shear modulus GLT (Msi).......................................................0.73

Poisson’s ratio νLT .................................................................0.31
NASA/TM—2011-217198 22

TABLE 7.—COMPARISON OF OBJECT LOADS BETWEEN HyperSizer AND FEA

Nx 

(lb/in.)

Ny 

(lb/in.)

HyperSizer FEA HyperSizer FEA

Top face combo –2219 –2219 248 244

Web –166 –166 –12 –13

Bottom face combo –2219 –2220 248 244

Figure 21.—Dimension of the RCS panel modeled using the new HyperSizer methods and FEA.

Figure 22.—Converged mesh used for RCS panel shown both with and without the foam elements.

Figure 23.—Static boundary conditions imposed to simulate biaxial loading on RCS panel.
NASA/TM—2011-217198 23

Figure 24.—Buckling boundary conditions imposed to simulate biaxial 

loading on RCS panel.

Figure 25.—FEA buckled mode shape for an RCS panel with no foam 

(i.e., a blade stiffened sandwich panel).

For eigenvalue buckling analysis, the same boundary conditions depicted in Figure 23 were imposed 

as the perturbation, and the buckling boundary conditions involved leaving the foam boundaries free, 

treating the y-boundaries of the shells as symmetric, and imposing simple support on the x-boundaries of 

shells, see Figure 24. Performing the buckling analysis first on a panel with the foam removed, a 

minimum eigenvalue of 0.234 resulted, with the mode shape shown in Figure 25. In this case, the 

presented solution predicts an eigenvalue (buckling load/applied load) of 0.24 for the web and 0.19 for the 

web. Clearly, from Figure 25, the FE solution indicates that the buckling of the web and facesheet are 

coupled. Considering the presented solution eigenvalue of the web, the presented solution is conservative 

with respect to FEA by 18 percent.

When the foam is included in the FEA buckling analysis, the minimum eigenvalue rises to 1.12, an 

increase of 4.8 times. The mode shape for this case is shown in Figure 26. The presented solution predicts 

a minimum eigenvalue (in the facesheet) of 0.49 using the effective stiffness K approach, and 1.00 using 

the Hetenyi K approach. These values are 56 and 9 percent conservative with respect to the FEA results, 

respectively. Varying the Young’s modulus of the foam (while maintaining the Poisson ratio), Figure 27

compares the effective stiffness K and the Hetenyi K predictions for the presented method with the FEA 

solutions for facesheet buckling of the RCS panel. As the foam material becomes stiffer, the effective 
NASA/TM—2011-217198 24

Figure 26.—FEA buckled mode shape for an RCS panel (including 

foam).

Figure 27.—Difference between the presented solution for facesheet buckling 

and the FEA predictions as a function of the foam stiffness for the effective 

stiffness and Hetenyi approaches for determining K.

stiffness approach becomes more conservative, while the Hetenyi approach becomes less conservative. It 

appears that to obtain the best agreement with FEA, while still remaining somewhat conservative, the 

Hetenyi approach is preferable, whereas, the effective stiffness approach is extremely conservative.

5.1.2 Sizing Results

To show the effects of the new sizing capability for RCS within HyperSizer, comparison has been 

made to two lower fidelity approaches used previously within HyperSizer to size RCS panels. The first 

approach treats the RCS panel like a honeycomb sandwich panel in HyperSizer, where the core is selected 

from a number of candidate materials whose properties are provided by the vendor. The facesheet is then 

sized independently, but, in the case of RCS, the web thickness, spacing, layup, and material cannot be 

sized/selected. Rather, effective, or smeared, properties are used for the core. In addition, this approach 

neglects any in-plane contribution of the core webs. For this approach, the core materials given in Table 8

were used as the candidate effective core materials.
NASA/TM—2011-217198 25

TABLE 8.—CANDIDATE CORE MATERIAL PROPERTIES USED IN 

THE EFFECTIVE CORE APPROACH TO SIZING RCS

Density 

(pcf)

Et

(ksi)

Ec 

(ksi)

Gw 

(ksi)

Gl

(ksi)

Ftu 

(psi)

Fsuw 

(psi)

Fsul 

(psi)

Fcus 

(psi)

WebCore A 4.1 26.1 26.1 1.88 44.7 272 89 234 352 

WebCore Light Bi 7.5 68.0 68.0 9 35 1641 145 473 1641 

TYCOR 126-C06 11.7 314 314 147 212 710 764 538 2000 

TYCOR 94-C1 3.9 23.1 23.1 1.90 37.5 305 60 231 355 

The second lower fidelity method for sizing RCS panels in HyperSizer involves treating the panel as 

a blade-stiffened sandwich panel within the code. The panel is then sized without foam, and the mass of 

the foam is added to the panel mass as a post-processing step. To account for the local buckling support of 

the foam, the loads in the facesheet and webs were permitted to be 300 percent of the buckling load 

calculated by HyperSizer for the unsupported local buckling case. This 300 percent factor was determined 

via trial and error to give reasonable results versus experimental observations, but it is clearly an ad hoc 

method. This blade-stiffened sandwich panel approach does allow the sizing of the web thickness and 

spacing, along with the material and layup selection, but the wrap layer is not accounted for in the 

facesheet combo. Note that the wrap layer could be manually added to the facesheet, but it would not be 

active in the sizing process.

To compare these two lower fidelity sizing methods with the new method presented, a panel level 

sizing was performed with loading similar to the acreage of NASA’s Ares V interstage. This is a 33 ft. 

diameter cylinder subjected primarily to axial compression, but with some hoop and in-plane shear load 

due to bending of the rocket stack during flight. The actual loads employed cannot be disclosed, but the 

axial compressive load is in the mid-thousands of lb/in, and the remaining loads employed for strength 

and buckling sizing are given with respect to the axial load Nx in Table 9. A 1.4 ultimate factor, a 1.0 

limit factor, and a 0.65 panel buckling knockdown were employed in the sizing. Effective laminates 

constructed from IM7/8552 open hole compression ply properties were used for the facesheets and webs, 

with a maximum of 75 percent 0° plies in the facesheets and 45 percent 0 ° plies in the webs. Four 

Rohacell (Ref. 20) foam material candidates, ranging from 2 to 6.9 lb/ft3 density, were considered. The 

x-direction buckling length of each sized panel was varied from 15 in. to 120 in. to simulate the effects of 

ring frame spacing on the panel areal weight. In an axially-compressed cylinder, the main function of the 

ring frames are to limit the buckling half-wave length to the distance between the rings. This reduced 

buckling length then allows the panels to be thinner and thus lighter.

TABLE 9.—NORMALIZED PANEL LEVEL LOADING IMPOSED ON 

THE REPRESENTATIVE ARES V INTERSTAGE ACREAGE PANEL

Nx Ny Nxy 

Strength –Nx –0.099 Nx –0.052 Nx

Buckling –0.47 Nx –0.098 Nx –0.026 Nx

Results for the Ares V interstage panel sizing are shown in Figure 28. The panel areal weights 

(weight per unit area) are plotted versus buckling length for the effective, or smeared, property approach, 

the blade-stiffened sandwich approach and for the newly implemented approach using the effective 

stiffness K and the Hetenyi K. It is noted that in all cases, the lightest effective core and foam material 

candidates were chosen. The areal weight increases nonlinearly for all approaches because the panel 

height increases due to the increasing buckling span length, but the height can increase in a weight 

efficient manner by increasing the low density core. The results show that the new HyperSizer method 

using the Hetenyi approach yields significantly lighter designs for the RCS panels compared to the other 

methods. The other methods are fairly close in areal weight, except at the higher buckling lengths, where 
NASA/TM—2011-217198 26

the new HyperSizer approach with the effective stiffness K diverges from the effective property and 

blade-stiffened approaches, which are the heaviest. Table 10 provides details of the sized panels for 

buckling lengths of 30-, 75-, and 120-in. As the buckling length increases, the effective core design tends 

towards a large panel height as this approach does not consider buckling of the webs, which becomes 

more problematic as the webs become tall. The blade stiffened sandwich panel design tends toward thick 

webs, indicating that, while the 300 percent local buckling factor may be reasonable for facesheet 

buckling, it is too conservative for the webs. The new HyperSizer concept using the effective stiffness K

tends toward thicker facesheets that the other approaches, a further indication that this approach may be 

too conservative for facesheet buckling. 

Figure 28.—Panel areal weight versus ring frame spacing for the Ares V interstage 

acreage panel sized using different methods.

TABLE 10.—PANEL SIZING RESULTS FOR ARES V INTERSTAGE ACREAGE PANEL

Buck L

30 in. 75 in. 120 in.

Eff. 

core

Blade New 

eff. K

New

Het. K

Eff. 

core

Blade New 

eff. K

Conc.

Het. K

Eff. 

core

Blade New 

eff. K

Conc.

Het. K

Areal weight (lb/ft2) 1.14 1.10 1.12 1.07 1.46 1.49 1.46 1.31 1.66 1.66 1.58 1.45

Panel height (in.) 1.0 1.1 1.0 1.1 2.0 2.0 1.7 2.0 2.8 2.4 1.9 2.3

FS thickness (plies) 9 8 9 8 9 9 11 8 9 10 12 9

Web thickness (plies) – 4 4 4 – 6 4 4 – 6 4 4

Web spacing (in.) – 1.1 1.2 1.2 – 1.7 1.7 1.4 – 2.0 2.0 1.7

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 20 40 60 80 100 120 140

Panel Areal Weight (psf)

Buckling Length (in.)

Effective Properties

Blade Stiffened Sandwich

New RCS HyperSizer Concept - Eff Stiffness K

New RCS HyperSizer Concept - Hetenyi K
NASA/TM—2011-217198 27

Figure 29.—NASA’s Ares V payload shroud FE model.

To compare the four approaches for sizing RCS panels for a full structure, the design of NASA’s 

Ares V payload shroud was considered. This large structure, shown in Figure 29, protects the payload 

during launch and ascent. The panels of the structure were divided into three components, the upper nose, 

lower nose, and barrel, each separated by a ring frame. Four longitudinal separation rails are present in the 

structure, but these are not sized to carry load as their main purpose is to enable separation of the four 

petals to reveal the payload. There are also five cutouts, each with a frame. In this case, unlike the 

interstage acreage panel sizing described previously, the loads vary over the structure and each panel 

component is sized to its design-to loads. The structure was subjected to six load cases: max. G plus 

thermal, max Q, and four max. Qα cases clocked at 90° around the circumference of the shroud. Because 

the payload shroud is at the top of the vehicle, the loads are significantly lower (5 to 20 percent) than 

those of the interstage. As in the interstage, a 1.4 ultimate factor, a 1.0 limit factor, and a 0.65 buckling 

knockdown were employed. Unlike the interstage, both the facesheet and webs were sized using 

[0/±45/90] IM7/977-3 effective laminate material properties. Again, the lightest effective core and lightest 

foam material candidates were always selected.

Figure 30 provides the average areal weight comparison for the four approaches for the Ares V 

payload shroud, while Table 11 to Table 13 provide the sizing details for the three panel components. 

Again, it is clear that the new HyperSizer concept, with the Hetenyi foundational stiffness, provides a 

significantly lighter-weight design than the other methods. Comparing this design to that using the 

effective foundational stiffness approach, the web spacing is much larger and the facesheet much 

thinner using the Hetenyi approach. This is expected as the effective stiffness approach is far more 

conservative for facesheet buckling. With the thicker facesheets and lower web spacing, the effective 

stiffness K approach panel height is smaller, but this is clearly a much less weight efficient design. The 
NASA/TM—2011-217198 28

blade-stiffened panel approach design is comparable in average areal weight to the new effective stiffness 

K approach, however, the panel height is higher, the facesheets are thinner, and the web spacing is lower.

Figure 30.—Average panel areal weight results for the Ares V payload 

shroud sized using different methods.

TABLE 11.—RCS PANEL DESIGN DETAILS FOR THE ARES V PAYLOAD SHROUD UPPER NOSE

Upper nose Eff. core Blade New eff. K New Het. K 

Areal weight (psf) 0.88 0.87 0.81 0.70 

Height (in.) 1.67 1.50 1.25 1.75 

Facesheet (plies) 4 4 7 4 

Web (plies) – 4 4 4 

Web spacing (in.) – 1.0 3.0 6.0 

TABLE 12.—RCS PANEL DESIGN DETAILS FOR THE ARES V PAYLOAD SHROUD LOWER NOSE

Lower nose Eff. core Blade New eff. K New Het. K 

Areal weight (psf) 0.88 0.74 0.77 0.60 

Height (in.) 1.67 1.0 0.75 1.25 

Facesheet (plies) 4 4 7 4 

Web (plies) – 5 4 4 

Web spacing (in.) – 1.0 4.0 6.0 

TABLE 13.—RCS PANEL DESIGN DETAILS FOR THE ARES V PAYLOAD SHROUD BARREL

Barrel Eff. core Blade New eff. K New Het. K 

Areal weight (psf) 0.96 0.79 0.80 0.64 

Height (in.) 1.67 1.25 0.75 1.0 

Facesheet (plies) 5 4 7 5 

Web (plies) – 4 4 4 

Web spacing (in.) – 1.0 2.0 6.0 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Eff. Core Blade Concept Eff. K Concept 

Hetenyi K

0.918

0.783 0.793

0.630

Average Panel Areal Weight (psf)
NASA/TM—2011-217198 29

5.2 Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) Panels

5.2.3 Verification and Validation Results

Verification studies for PRSEUS methods were carried out on a PRSEUS panel fabricated and tested 

by Boeing. The overall panel dimensions of the panel are 80-in. long by 42-in. wide with a frame spacing 

of 20 in. and a stringer spacing of 6 in. (7 stringers across the panel width). The as-fabricated panel is 

shown in Figure 3. The lamina used to make up the facesheet, stringer, and flange laminates consisted of 

“stacks” of AS4 fibers infused with epoxy resin. Each stack was 0.052 in. thick and consisted of 7 plies as 

shown in Table 14.

TABLE 14.—FACESHEET, STRINGER,

AND FLANGE LAMINATE LAYUPS FOR

THE SIMULATED PRSEUS PANEL

Ply Thickness Angle

7 0.0056 +45

6 0.0056 –45

5 0.0117 0

4 0.0056 90

3 0.0117 0

2 0.0056 –45

1 0.0056 +45

The stringer dimensions are shown in Figure 31. The frame dimensions are shown in Figure 32. Two 

different panels were fabricated with identical stringers and frames. The first panel had a two-stack skin 

with a thickness of 0.104 in. and the second panel had a one-stack skin with a thickness of 0.052 in. The 

HyperSizer verifications described below used the second configuration with 0.052 in. thick facesheets.

Further fabrication details along with material stiffness and failure properties can be found in

References 4 and 21.

Figure 31.—Stringer dimensions for the simulates PRSEUS panel. 
NASA/TM—2011-217198 30

Figure 32.—Frame dimensions for the simulated PRSEUS panel. 

5.2.3.1 FEA Verification of Thermoelastic Formulation

The ABD matrix verification is performed by constructing a discrete FE model of a PRSEUS panel

using plate elements with PCOMP composite properties and beam elements representing the stiffener rod.

Four separate load conditions, as shown in Figure 33, were applied to obtain load-strain and momentcurvature response to back-out panel level ABD matrices.

After applying these four loading conditions, the strains, curvatures and resultant loads were all 

extracted from the FEA results and used to calculate ABD terms. These were then compared to 

HyperSizer results of the same panel. We should emphasize that although the panel FE models were 

generated using HyperSizer, there are no HyperSizer specific constructs in the FE model. In other words, 

the model uses actual ply stiffness properties and PCOMPs to represent all of the laminates. The panel 

strain response to the four load cases are listed in Table 15 for HyperSizer and FEA. 

The loads and strains can be used to back-out panel ABD terms by expanding the terms of the ABD 

matrix,

11 12 13 11 12 13

21 22 23 21 22 23

x x y xy x y xy

y x y xy x y xy

NA A A B B B

NA A A B B B

=++ ++ +

=++ ++ +

εεκ κκκ

εεκ κκκ

For Case 1, all strains and curvatures are zero except for εx, therefore the equations are reduced to:

11 11

21 21 12

/

/

x x x x

y x y x

NA AN

NA AAN

= ⇒=

= ⇒ ==

ε ε

ε ε
NASA/TM—2011-217198 31

The other ABD terms can be backed out from the remaining load cases as follows. The comparisons 

shown in Table 16 indicate a good match between panel level response between HyperSizer and FEA for 

the PRSEUS panel. 

Case 1: Applied Nx Case 2: Applied Ny

Case 3: Applied Mx Case 4: Applied My

Figure 33.—Load conditions applied to the simulated PRSEUS panel.

TABLE 15.—COMPARISON OF THE PANEL LEVEL LOADS AND 

STRAINS FOR THE SIMULATED PRSEUS PANEL FROM 

FEA AND THE NEW HyperSizer CAPABILITY

LC 1—Applied Nx

FEA HyperSizer Difference

Nx (lb/in.) 2,381 2,381 0.0%

Ny (lb/in.) 264 252 4.6%

ex (μin./in.) 1,596 1,642 –2.9%

LC2—Applied Ny

FEA HyperSizer Difference

Nx (lb/in.) 140 138 1.6%

Ny (lb/in.) 1,250 1,250 0.0%

ey (μin./in.) 842 882 –4.7%

LC 3—Applied Mx

FEA HyperSizer Difference

Mx (lb-in./in.) 1,000 1,000 0.0%

kx (×106 in–1) 1,401 1,478 –5.5%

LC2—Applied Ny

FEA HyperSizer Difference

My (lb-in./in.) 1,000 1,000 0.0%

ky (×106 in–1) 135 142 –5.3%

x

y
NASA/TM—2011-217198 32

TABLE 16.—COMPARISON OF THE ABD TERMS FOR THE 

SIMULATED PRSEUS PANEL FROM FEA AND 

THE NEW HyperSizer CAPABILITY

LC no. Formula FEA HyperSizer Difference

A11 1 Nx/ex 1,491,942 1,450,016 2.8%

A12 1 Ny/ex 165,481 156,345 5.5%

A22 2 Ny/ey 1,483,805 1,417,502 4.5%

A21 2 Nx/ey 165,481 156,345 5.2%

B11 1 Mx/ex 688,367 647,876 5.9%

B22 2 My/ey 1,856,107 1,788,691 3.6%

D11 3 Mx/kx 713,840 676,788 5.2%

D22 4 My/ky 7,416,433 7,044,432 5.0%

In addition to panel level response, loads at the object level are also important for strength, local 

buckling, and crippling failure analyses. Figure 34 shows a comparison between the FEA extracted local 

loads and HyperSizer values. A summary of the internal load comparison between FEA and HyperSizer is 

shown in Table 17.

Figure 34.—Comparison of the internal loads in the simulated PRSEUS panel from FEA and the new HyperSizer 

capability.

TABLE 17.—COMPARISON OF THE INTERNAL LOADS IN THE 

SIMULATED PRSEUS PANEL FROM FEA AND 

THE NEW HyperSizer CAPABILITY

Object Nx loads FEA HyperSizer Percent diff.

Open span (lb/in.) –458 –440 3.9

Bonded combo, stringer –2097 –2150 2.5

Stringer web –1570 –1561 0.5

Stiffening rod (lb) –4267 –4334 1.5
NASA/TM—2011-217198 33

5.2.3.2 HyperSizer Prediction of Postbuckling Strength

In the HyperSizer analysis of this panel, an applied axial load of 2381 lb/in. was applied to the panel.

With a panel width of 42 in., this corresponds to a total applied load of 100 kips. The ultimate load of the 

panel is found from the ultimate margin of safety as Fult = Fapplied (MSult – 1). The HyperSizer margins of 

safety for this panel are shown in Figure 35.

The ultimate margin of safety is panel torsional stability of 1.22. This yields a failure load of

( ) ( ) applied 1 1.22 1 100 kips 222 kips ult N MS N x ult x = + = +× = (26)

Table 18 summarizes the margins and corresponding loads for various failure modes.

TABLE 18.—MARGINS CALCULATED BY HyperSizer

FOR THE SIMULATED PRSEUS PANEL

Failure mode Margin Panel load 

(kips)

Torsional buckling 1.224 222

Crippling 1.874 287

Frame span buckling 2.20 320

Material strength (max strain) 3.6 460

Panel buckling (full 80x42 panel) 4.49 549

Figure 35.—Simulated PRSEUS panel margins of safety.
NASA/TM—2011-217198 34

Figure 36.—Abaqus FE model prediction for the postbuckling load versus strain response for 

the simulated PRSEUS panel.

5.2.3.3 FEA Verification of Postbuckling Strength

To verify any postbuckling result, linear static and eigenvalue FEA is no longer sufficient. The user 

must rely on a geometric nonlinear finite element analysis to verify any post-buckled results. The same 

PRSEUS discrete model FE model from the previous section was analyzed using geometric nonlinear 

analysis in ABAQUS.

The postbuckling load versus strain response is shown in Figure 36. In nonlinear postbuckling 

analysis, it is difficult to ascertain what constitutes a “buckling” event. In the results shown here, two 

events are used to determine when buckling occurs. First, negative eigenvalue buckling refers to the 

solver reporting negative eigenvalues while decomposing the stiffness matrix for inversion. The first 

negative eigenvalues shown in the following figure indicate the onset of local buckling. A secondary 

event that indicates the presence of local buckling is a change in the panel-stiffness matrix. These are 

shown below and indicate secondary buckling events such as a mode change, or the final panel collapse.

In the current results, three principle responses were detected. First, local buckling onset occurred at 

approximately 2570 lb/in. (108 kips). This is slightly higher than the load, 85 kips, predicted from linear 

eigenvalue analysis. A secondary event occurs when the local buckling modes change from two to three 

half-waves at approximately 159 kips. Finally the panel continues loading to a final collapse load of 

229 kips. This compares favorably to the postbuckled HyperSizer Torsional value of 222 kips.

The ultimate failure mode from the nonlinear analysis can be determined by examining the deflected 

mode shapes. First, the initial local buckling mode shape at a load of 108 kips. The local buckled shapes 

can be seen in the second and fourth bays and are beginning to develop in the third, Figure 37. These 

mode shapes match the linear eigenvalue mode shapes (not shown). The color contours represent the

relative magnitude of out-of-plane deflection.

The second event is the mode shift that occurs at approximately 159 kips. Notice that there are now 

three half-waves in the 2nd and 4th span and two half waves in the center span, Figure 38. Also notice 

that we are starting to see a slight perturbation of the stiffener.

The final result snapshots for this analysis are at a point just before final collapse. This result is at 

229 kips. Notice that there is substantial deformation of the straight stiffener path as the stiffeners are 

starting to tip substantially, Figure 39.

Linear/Static 

Response 

Local 

Buckling 

Onset 

Panel Collapse 

Apparent Local 

Mode Change

Linear Eigenvalue Local Buckling 
NASA/TM—2011-217198 35

Also of note is the deformed shape of the panel shown from the side, Figure 40. As the stiffeners tip 

the load that they are carrying is beginning to offload from the very stiff rod into the facesheet. As this 

happens the effective bending stiffness of the panel is rapidly diminishing and the panel is beginning to 

take on a flexural (i.e., panel) buckling mode shape.

Figure 37.—First mode shape present in the Abaqus FEA 

local postbuckling simulation of the PRSEUS panel.

Figure 38.—Second mode shape present in the Abaqus FEA 

local postbuckling simulation of the PRSEUS panel.

Figure 39.—Final mode shape in the Abaqus FEA local 

postbuckling simulation of the PRSEUS panel.
NASA/TM—2011-217198 36

Figure 40.—Final mode shape in the Abaqus FEA local postbuckling simulation of 

the PRSEUS panel, viewed from the side.

Figure 41.—Plot of linear elastic load-strain versus nonlinear postbuckling load-strain.

So, in summary, the nonlinear FEA shows a torsional buckling mode of the stiffeners which leads very 

quickly to panel collapse by overall panel buckling. The load level of collapse is 229 kips which 

compares favorably to HyperSizer’s predicted failure mode of torsional buckling at 222 kips.

5.2.3.4 Validation to Test Data

The single stack PRSEUS panel was tested to failure at NASA Langley in 2009 where the panel was 

subjected to uniform compressive load. One of the purposes of the test was to assess the damage tolerant 

capability of PRSEUS, therefore the panel was impacted prior to testing. Local buckling of the skin was 

observed in the test at just over 100 kips and the panel ultimate failure occurred at 199 kips. In Figure 41, 

the ABAQUS nonlinear response is shown as the orange line, compared with HyperSizer’s nonlinear 

response shown as a blue line. In addition to the predicted failure load of 222 kips, the plot also shows 

HyperSizer’s prediction for local buckling of the skin, stiffener crippling and frame span buckling.
NASA/TM—2011-217198 37

Figure 42.—Ares V Interstage internal axial (Nx) loads due to flight conditions.

5.2.4 Sizing Results 

To illustrate the sizing capability of the new HyperSizer PRSEUS capability, a PRSEUS Panel for the 

NASA Ares V Interstage has been sized. The primary load supported by the NASA Ares V Interstage is 

axial compression from a combination of vertical acceleration and the bending moment. However, two 

other loadings must be considered: (1) hoop tension caused by the internal pressurization (2) compressive 

hoop load caused by crushing pressure. This combination of biaxial loads including hoop compression 

makes the PRSEUS panel concept, with its transverse frames especially desirable. To determine static 

loads, the external axial, moment, and shear loads are applied to the top of the cylindrical Interstage. The

reaction loads are derived at the bottom of the Interstage. Figure 42 shows how the flight loads are 

applied to derive the internal loads. See Reference 22 for more details on loading and sizing results.

Though the loading is statically determinate, FEA is used to resolve the external flight loads into 

internal element loads, that includes the effects of ringframe hoop load sharing. The maximum line load at 

the base of the Interstage results from the combination of axial and moment load. During this study 

NASA required the entire barrel is to be the same design—so the entire barrel from bottom to top is sized 

to the maximum line load experienced at station B. 

Optimum PRSEUS results derived during the Ares V interstage study (Ref. 22) are shown in

Figure 43. PRSEUS has one advantage over other panels concepts in that frame is integral to the stiffened 

panel, where other panel concepts require a separate ringframe for global stability. The optimum PRSEUS 

design has a frame spacing of 52 in. and a stringer spacing of 7.5 in. The unit weight is 2.02 lb/ft2

.

Margins of safety for each failure analysis in the HyperSizer Failure tab are shown in Figure 44. With 

the given panel sizing, the panel is controlled by global panel buckling. Because this concept adds 

stitching to the flange to skin bondline, it is allowed to postbuckle (LPB). Initial skin buckling is allowed 

at 75 percent limit load.

*Used to normalize 

internal loads

Constrained at B
NASA/TM—2011-217198 38

Figure 43.—HyperSizer sizing results for the PRSEUS Ares V interstage acreage panel.

Figure 44.—HyperSizer margin of safety results for the PRSEUS Ares V interstage acreage panel.

6.0 Conclusions

New design and sizing capabilities have been developed and incorporated into the HyperSizer 

Structural Sizing Software for two novel composite panel concepts. Reinforced core sandwich (RCS) 

panels combine aspects of foam core sandwich panels and stiffened panels in a concept that includes 

integral composite webs for optimum through-thickness shear capabilities and excellent damage 

tolerance. Boeing’s Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) panels rely on 

precured unidirectional composite rods for high axial stiffness, integral foam core frames of transverse 

support, and stitching for superior damage tolerance. Both concepts are resin-infiltrated and oven-cured, 

which can provide manufacturing efficiencies. This paper outlines the new methods that have been 

developed and incorporated into HyperSizer to determine the local forces, stresses, and strains and to 

predict the failure loads associated with the many failure modes that have been observed for these new 

composite panel concepts. Verification and validation results been shown for the new methods, and 
NASA/TM—2011-217198 39

example sizing results have illustrated the utility of these new HyperSizer capabilities. Both RCS and 

PRSEUS panels, as available structural concepts within HyperSizer, can now be applied widely in 

lightweight composite structural design.

References

1. HyperSizer Structural Sizing Software, Collier Research Corp., Hampton, VA, 

http://www.hypersizer.com, 2010.

2. Stoll, F., Day, S., Campbell, S., Banerjee, R., Sheppard, M., and Lang, E., “Advancements in 

Engineered Composite Sandwich Core Materials,” SAMPE 2006, May, Long Beach, CA, 2006.

3. WebCore Technologies, Inc., Miamisburg, OH, http://www.webcoreonline.com, 2010.

4. Velicki, A and Thrash, P., “Advanced Structural Concept Development Using Stitched Composites,” 

49th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 

Schaumburg, IL, April 2008, AIAA 2008-2329.

5. Bednarcyk, B.A., Arnold, S.M., Collier, C.S., and Yarrington, P.W. “Preliminary Structural Sizing 

and Alternative Material Trade Study for CEV Crew Module,” 48th AIAA/ASME/ASCE/AHS/ASC 

Structures, Structural Dynamics, and Materials Conference, Honolulu, HI, April 2007, AIAA 2007-

2175.

6. Bednarcyk, B.A., Arnold, S.M, and Hopkins, D.A., “Design of Fiber Reinforced Foam Sandwich 

Panels for Large Ares V Structural Applications,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials Conference, Orlando, FL, April, 2010, AIAA 2010-2781.

7. Zalewski, B.F. and Bednarcyk, B.A., “ACT Payload Shroud Structural Concept Analysis and 

Optimization,” NASA/TM—2010-216942, 2010.

8. Berg, J.S. and Higgins, J., “VARTM Infusion: Processing Large Carbon/Epoxy Space Structures Out 

of the Autoclave,” SAMPE Journal, Vol. 44, No. 6, pp. 41-44, 2008.

9. Yovanof, N.P, Velicki, A., and Li, V. “Advanced Structural Stability Analysis of a Noncircular, 

BWB-Shaped Vehicle” 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and 

Materials Conference, Palm Springs, CA, May, 2009, AIAA 2009-2452.

10. Ley, R. P., Lin, W., Mbanefo, U., “Facesheet Wrinkling in Sandwich Structures”, NASA/CR—1999-

208994, 1999.

11. Whitney, J.M., Structural Analysis of Laminated Anisotropic Plates, Technomic, Lancaster, PA, 

1987.

12. Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, McGraw-Hill, 1961.

13. Hetenyi, M., Beams on Elastic Foundation, University of Michigan Press, 1946.

14. Collier, C., “Stiffness, Thermal Expansion, and Thermal Bending Formulation of Stiffened, FiberReinforced Composite Panels,” 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural 

Dynamics, and Materials Conference, La Jolla, April 1993, AIAA 93-1569.

15. Collier, C., “Thermoelastic Formulation of Stiffened, Unsymmetric Composite Panels for Finite 

Element Analysis of High Speed Aircraft,” 35th AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials, Hilton Head, SC, April 1994, AIAA 94-1579.

16. Collier, C., Yarrington, P., and Van West, B., “Composite, Grid Stiffened Panel Design for Post 

Buckling Using HyperSizer” 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, 

and Materials Conference, Denver, CO, 2002.

17. Collier, C., Yarrington, P., Gustafson, P., and Bednarcyk, B., “Local Post Buckling: An Efficient 

Analysis Approach for Industry Use,” 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural 

Dynamics, and Materials Conference. Palm Springs, CA, 2009.

18. Argyris, J., Flexural-Torsion Failure of Panels. Aircraft Engineering, 1954.

19. Seydel, E., “On the Buckling of rectangular isotropic and or orthogonal-isotropic plates by tangential 

stresses,” Ing Archiv., 1933. 

20. Evonic Industries, Rohacell IG/IG-F Datasheet, 

http://www.rohacell.com/en/performanceplastics8344.html, Aug. 2009.
NASA/TM—2011-217198 40

21. Jegley, D. C., Alexander V., and Hanson, D. A., “Structural Efficiency Of Stitched Rod-Stiffened 

Composite Panels With Stiffener Crippling,” 49th AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials Conference, Schaumburg, IL, April 2008.

22. Collier, C., Ainsworth, J., Yarrington, P., and Lucking, R., “Ares V Interstage Composite Panel 

Concept and Ringframe Spacing Trade Studies,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials Conference, Orlando, FL, April 2010.

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-12-2011 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Efficient Design and Analysis of Lightweight Reinforced Core Sandwich and PRSEUS 

Structures 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Bednarcyk, Brett, A.; Yarrington, Phillip, W.; Lucking, Ryan, C.; Collier, Craig, S.; 

Ainsworth, James, J. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 944244.04.02.03 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-17883 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2011-217198 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 39 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Design, analysis, and sizing methods for two novel structural panel concepts have been developed and incorporated into the HyperSizer 

Structural Sizing Software. Reinforced Core Sandwich (RCS) panels consist of a foam core with reinforcing composite webs connecting 

composite facesheets. Boeing’s Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) panels use a pultruded unidirectional 

composite rod to provide axial stiffness along with integrated transverse frames and stitching. Both of these structural concepts are ovencured and have shown great promise applications in lightweight structures, but have suffered from the lack of efficient sizing capabilities 

similar to those that exist for honeycomb sandwich, foam sandwich, hat stiffened, and other, more traditional concepts. Now, with accurate 

design methods for RCS and PRSEUS panels available in HyperSizer, these concepts can be traded and used in designs as is done with the 

more traditional structural concepts. The methods developed to enable sizing of RCS and PRSEUS are outlined, as are results showing the 

validity and utility of the methods. Applications include several large NASA heavy lift launch vehicle structures. 

15. SUBJECT TERMS

Sandwich structures; Buckling; Panels; Failure; Composite structures; Structural design; Ares V; Finite element method; HyperSizer 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

48 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18