# Presentation: 677616

## A Formulation for a 1-D Finite Element With Anisotropic Wall Material Properties

- Victor Eyo
- Mechanical Systems Branch (Code 548)
- GSFC, Wallops Flight Facility

## Motivation

- Old college assignment
- Lack of 1-Dimensional finite element capable of anisotropic material property input
- Possible research tool for balloon structural analyses
- Closed form solution eliminates singularities encountered with traditional shell elements

- FEMCI 2006 Oct 25 & 26

**Notes:**
I will talk about the ISS design analysis.  These really are very simple structures.  However, their design and analyses are becoming more and more complex because of demands for light weight, optimization and other factors.

I will use the very successful record breaking 2004 CREAM Antartica mission as an example.

In addition, I hope that after this presentation, I would have successfully introduced some of us to just a small part of the kinds of things that Code 548 does at Wallops.  Here’s what we do and we work closely with Code 820, the BPO.

## Geometry & Loading

- Geometry Considered
- Thin walled cantilevered cylindrical tubes
- Length, L
- Radius r
- Generalized coordinate, (r,) pair
- Loading
- Loaded at free end via some kind of reinforcement system
- Shear loads, Vx & Vy
- Moments, Mx & My
- Torque, T
- Axial load, P

- FEMCI 2006 Oct 25 & 26

**Notes:**
Scientific ballooning is becoming more and more popular for several reasons, cost being the primary.  We can fly 8000lb systems to as high as 125K feet. Two problems, however, still haunt balloon flights – they depend on the weather for lunch and they depend on the winds for flight trajectory – can’t control them even if you wanted to. Scientific balloons are very large structures.  

Fully inflated, its volume is 39.57mcf and weighs 4,055lb.  It will float to 125Kft carrying a payload of 4153lb on a film that’s 0.8mil thick

## Constitutive Equation

- Assumptions
- Wall bending stiffness neglected
- Shape of cross-section maintained during deformation
- Reinforcement system (spar, web,...) for proper load distribution
- Resulting Analysis Model
- Circumferential strains disappear
- Wall considered membrane in plane stress
- State of stress at any point on the wall can be expressed as

- FEMCI 2006 Oct 25 & 26

**Notes:**
The ISS is the structural support system for the science payload.

We work very closely with the NSBF in Palestine, TX. They prescribe ISS design parameters, certify the ISS as flight worthy, regardless of who builds it, and are responsible for all phases of flight operations.

## Constitutive Equation

- In terms of stress resultant

*N*: “tension flow”
*q*: shear flow

- FEMCI 2006 Oct 25 & 26

**Notes:**
The ISS is the structural support system for the science payload.

We work very closely with the NSBF in Palestine, TX. They prescribe ISS design parameters, certify the ISS as flight worthy, regardless of who builds it, and are responsible for all phases of flight operations.

## Constitutive Equation

- Inverting

**i(***,z*): elastic constants, in general will vary with *** and z*, but assumed constant here

- FEMCI 2006 Oct 25 & 26

## The n-Ply Symmetric Laminate

- Laminate Stress Strain Relationship

*Q**ij*(***k*) : In-plane global stiffness matrix

- 1

- 2

- 

- FEMCI 2006 Oct 25 & 26

**Notes:**
Cream is a cosmic ray experiment that was launched in December 2004 at the NSF base in McMurdo, in Antartica.  It turned out to be a record breaking flight.

The initial ISS design and analysis for the CREAM mission was performed by Swales Aerospace.  When I joined this project, Swales was at the tail end of finalizing their FEA on the structure.  They used NASTRAN (71) and did a very good job of representing the structure

(click to show structure)

Describe Swales model
Here’s the initial design with the science components shown

## The n-Ply Symmetric Laminate

- Expand
- Solve
- Compare

- FEMCI 2006 Oct 25 & 26

**Notes:**
Some details of the Swales design.

(Click to show manufactured piece)

Here’s a picture of the fabricated and assembled corner piece assembly

## Wall Displacement

- In-plane
- Displacements
- Rotations
- Small displacement theory

- Out of plane
- Displacements & rotations assumed to be of form

- Assume *k=1 *for this work

- FEMCI 2006 Oct 25 & 26

**Notes:**
I mentioned earlier that NSBF dictates the loading conditions of these systems.  The driving factor is safety – parts can yield but are not allowed to fall off or break!!!  At the end of the science experiment, the balloon craft & flight train are separated from the balloon vehicle. The rest of the flight train includes the ISS, science payload and a NSBF designed parachute and rigging system.  This entire assembly free-falls and eventually drifts to earth by parachute.  During this free fall, when the parachute deploys a shock load is imparted to the entire structure from the chute, via the attachment cables.  NSBF prescribes an equivalent static load for this phenomena, based on safety, historical data and heavy lift industry practices.

## Stress-Displacement Relationship

-  Linearized stress-displacement relationship
- Ref: Reissner, E., *On the Variational Theorem of Finite Elastic Deformations*, **Journal of Mathematics and Physics**, 32;129-135, July 1953
- Libove, Charles, *On the Stiffness, Stresses and Buckling Analysis of Corrugated Shear Webs*, In Wei-Wen Yu (Editor), **Second Specialty Conference on Cold Formed Steel Structures: Current Research and Design Trends**, pages 259-302, October 1973

- FEMCI 2006 Oct 25 & 26

**Notes:**
The first load case assumes that the gondola........The requirement here is to apply a 10G body load on the system.

## Displacements & Twist

-  Substitute for *u(****,z)*
-  Extract differential equations & natural 	boundary conditions
- Derive Total Potential Energy () of beam system
- Minimize the TPE
- requires its first variation =0
-  Solve DEQs applying prescribed boundary 	conditions

- FEMCI 2006 Oct 25 & 26

**Notes:**
The rational for load cases 3 & 4 are similar to that for the previous load case, except that in this case an assumption of rotation is made – a 45 degree angle is imposed.  Here again, depending on symmetry, this may be 8 different load cases.

## Displacements & Twist

- P

- FEMCI 2006 Oct 25 & 26

**Notes:**
I’ll step back in time here just for a moment.

The fabricated structure was delivered to WFF in Q3 2003, along with FEA files.  By Q4 2003, we had completed the model verification, and some updates based on the response of the fabricated structure to some static and dynamic tests.

As most of you know quite well, scientists are perfectionists when it comes to their science,  However, things like mass and power budgets to them seem like minor problems that can be resolved magically the night prior to launch.   So, no surprise that in 2004, we were geared up for an onslaught of new demands.  Here are the big ones

Click to show changes with sound effects.
	The mass requirement for ballast went up 35%, but that was OK ‘cause the net effect moved the system CG down which was a good thing.

The CDM's mass dropped 39% but it's CG was way off.

Now, the solar array was one of the most difficult pieces to integrate into the original FEA model.  Though its mass dropped by 34%, its size and location completely rendedered the structure very unsymmetrical.

The TDRSS antennae and its attachments came in at +82% and its location changed some.

Now we were all very happy with this TRD which cae in at -15% and maintained its location.  The second TRD, however, gave us the most problem.  With a 63% increase in mass it caused some problems as will be seen soon.

This table basically summarizes how our mass and inertias evolved.

## NASTRAN Model

-  Wall: QUAD4 Elements
-  586 nodes; 574 Elements
-  z axis used for orientation reference
-  Membrane and bending coupling

-  RBE3 rigid elements used to 	simulate displacements at	section mid-node

-  Capped Free end: 	QUAD4 with high stiffness

- FEMCI 2006 Oct 25 & 26

**Notes:**
Here's a FEMAP rendition of the major components that changed.  The solar array, the legs with crush pads and heaters, and the CDM assembly.

## Results

-  Tube Geometry
- r=0.8in
- t=0.04in
- L=14.0in
- Tube wall
- AL2024-T4
- Isotropic
- Homogenous
- Layered Composite Laminates
- E-Glass/Epoxy [(0/±45/90)]s
- T300/5208 Gr/E [(+20/-70)2]s

-  Loading
- Vx=Vy=10.0lb
- Mx=My=60.0in-lb
- T=123.0in-lb
- P=480.0lb

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results –AL2024-T4

- 1=0.424
- 2=0.0
- 4=0.159

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – AL2024-T4

- 1=0.424
- 2=0.0
- 4=0.159

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – AL2024-T4

- 1=0.424
- 2=0.0
- 4=0.159

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – E-Glass/Epoxy

- 1=0.221
- 2=0.0
- 4=0.090

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – E-Glass/Epoxy

- 1=0.221
- 2=0.0
- 4=0.090

- r=51.5%

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – E-Glass/Epoxy

- 1=0.221
- 2=0.0
- 4=0.090

- r=5.7%

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – T300/5208

- 1=0.380
- 2=-0.129
- 4=0.089

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – T300/5208

- 1=0.380
- 2=-0.129
- 4=0.089

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Results – T300/5208

- 1=0.380
- 2=-0.129
- 4=0.089

- FEMCI 2006 Oct 25 & 26

**Notes:**
This is a solid model of the upper instruments from the U of Chicago.  Here is a fringe plot of associated stresses and deformations for the worse case loads

In the last slide I pointed out that we had the most problem with the top TRD.  Well, it was a big problem - massive fastener failures at practically every joint of the top structure!!!

Turned out that science had used non flight certified fasteners at critical joints.  And to make matters worse, we couldn't access these locations.  If we could access them, we could have replacem them with higher strength fasteners and that would have done it.

## Conclusion

- Work in progress – no major conclusions
- Possible path to developing a 1-D finite element with anisotropic material properties

- FEMCI 2006 Oct 25 & 26

**Notes:**
Here's the interaction curve for the failed 1⁄4-inch fasteners.  We see here that the problem is easily resolved by increasing the fastener size.  This worked well for locations where the fasteners there was access to the fasteners.  In other cases as will be seen seen next, it was a challenge.