bluuebunny/crossref_metadata_2025 huggingface dataset:
Stochastic Estimation of Sub-Grid Scale Motions
Authors: Adrian R. J.
Published: April 2009

The problem of relating the resolved scale motions in a large eddy simulation to the non-resolved sub-grid scale motions is considered from the view point of stochastic estimation. Algorithms governing the large scale field are derived by requiring minimum mean square prediction error at each time step. Possible forms for quasi-homogeneous regions such as Smagorinski’s model are analyzed.
Algebraic Growth and Streak Formation in Shear Flows
Authors: Landahl Marten T.
Published: April 2009

By examination of the long-term behavior of an initial three-dimensional and localized disturbance in an inflection-free shear flow a detailed study of the algebraic instability mechanism of an inviscid shear flow (Landahl, 1980) is carried out. It is shown that the vertical velocity component will tend to zero at least as fast as 1/t whereas, as a result of a nonzero liftup of the fluid elements, the streamwise disturbence velocity component will tend to a limiting finite value in a convected frame of reference. For an initial disturbence having a nonzero net vertical momentum along a streamline, the streamwise dimension of the disturbed region is found to grow indefinitely at a rate set by the difference between the maximum and minimum velocities in the parallel flow. The total kinetic energy of the disturbence therefore grows linearly in time through the formation of continuously elongating high-speed or low-speed regions. In these, internal shear layers are formed that intensify through the mechanism of spanwise stretching of the mean vorticity. The effect of a small viscosity is felt primarily in the shear layers so as to make them diffuse and eventually cause the disturbence to decay on a viscous time scale. For the streaky structures near a wall the horizontal pressure gradients are found to be small, making possible a simple approximate treatment of nonlinearty. Such an analysis suggests the possibility of the appearance of a rapid outflow event (“bursting”) from the wall that may occur at a finite time inversely proportional to the amplitude of the initial disturbance. On basis of the analysis presented it is proposed that algebraic growth is the primary mechanism for the formation of streaks in laminar and turbulent shear flows.
Models Based on Dynamical Features of the Wall Layer
Authors: Walker J. D. A.
Published: April 2009

Recent experimental and theoretical results related to the turbulence production process near a wall are reviewed. It is argued that the principal element of boundary-layer turbulence is the convected hairpin vortex and that bursting of the wall-layer flow is a viscous-inviscid interaction provoked by the adverse pressure gradient due to the vortex. The consequences of this picture for the development of models for the mean near-wall flow are discussed. Recent models for the mean wall-layer velocity profile, in both two- and three-dimensional boundary layers, which are based on the dynamical picture presented here, are reviewed.
Nonlinear Dynamics, Chaos, and Mechanics
Authors: Holmes Philip
Published: April 2009

Nonlinear Dynamics or “Chaos Theory” is an ill-defined but energetic and rapidly developing subject which cuts across the boundaries of traditional disciplines. In this review, I describe a small part of it: some of the analytical approaches to nonlinear differential equations which have been developed in the last ten to fifteen years. I illustrate them with applications in solid and fluid mechanics.
Use of Experimental Data for an Efficient Description of Turbulent Flows
Authors: Aubry N.
Published: April 2009

The proper orthogonal decomposition (POD), also called Karhunen-Loe`ve expansion, which extracts ‘coherent structures’ from experimental data, is a very efficient tool for analyzing and modeling turbulent flows. It has been shown that it converges faster than any other expansion in terms of kinetic energy (Lumley 1970). First, the POD is applied to the chaotic solution of the Lorenz equations. The dynamics of the Lorenz attractor is reconstructed by only the first three POD modes. In the second part of this paper, we show how the POD can be used in turbulence modeling. The particular case studied is the wall region of a turbulent boundary layer. In this flow, the velocity field is expanded into POD modes in the normal direction and Fourier modes in the streamwise and spanwise directions. Dynamical systems are obtained by Galerkin projections of the Navier Stokes equations onto the different modes. Aubry et al. (1988) applied the technique to derive and study a ten dimensional representation which reproduced qualitatively the bursting event experimentally observed. It is shown that streamwise modes, absent in Aubry et al.’s model, participate to the bursting events. This agrees remarkably well with experimental observations. In both examples, the dynamics of the original system is very well recovered from the contribution of only a few modes.
Transition in the Failure Behavior of Dynamically Shear Loaded Cracks
Authors: Kalthoff J. F.
Published: April 2009

An experimental technique is presented for subjecting cracks to high rates of shear (mode-II) loading. By means of the shadow optical method of caustics, the dynamic crack tip loading conditions are investigated for both the phase of loading and the subsequent phase of failure. A failure mode transition is observed when the loading rate exceeds a certain limit. At low rates failure is controlled by fracture processes. At high rates, failure is controlled by the formation of adiabatic shear bands, a process not considered by fracture mechanics so far.
Stability and Imperfections in Quasistatic Viscoplastic Solutions
Authors: Belytschko T. , Moran B. , Kulkarni M.
Published: April 2009

The effect of imperfections on the structure of shear bands in strain-softening viscoplasticity is studied via a closed form solution. The stability of various solutions is then examined by varying the data through imperfections. It is shown that a step-function imperfection, such as commonly used in finite element solutions, leads to a step-function shear strain field, which is an unstable solution. Arbitrary C0 and C1 imperfections lead to C0 and C1 strain fields, respectively. Fourier analyses show that the imperfection scales the response of the viscoplastic material: the Fourier spectrum of the strain field is strongly influenced by the Fourier spectrum of the imperfection.
Analyses of Dynamic Ductile Crack Growth
Authors: Tvergaard V. , Needleman A.
Published: April 2009

Analyses of dynamic ductile crack growth are discussed where the material’s constitutive description allows for the possibility of a complete loss of stress carrying capacity. The analyses are based on a viscoplastic constitutive relation for a progressively cavitating solid and two populations of void nucleating particles are represented; large inclusions that nucleate voids early in the deformation history and small particles that require large strains before cavities nucleate. Within this framework fracture arises as a natural outcome of the deformation process. The computed crack growth velocities are entirely based on the ductile failure predictions of the material model. Thus, the calculations are free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for various conditions and for various values of material parameters.
Experimental Measurement of the Temperature Rise Generated During Dynamic Crack Growth in Metals
Authors: Zehnder Alan T. , Rosakis Ares J.
Published: April 2009

During the high speed propagation of cracks, large temperature increases occur at the crack tip due to the intense dissipation of plastic work there. This increased temperature may have a significant effect of the material’s dynamic fracture toughness. An experimental investigation of the temperature fields at the tip of dynamically propagating cracks in 4340 steel was performed using a focused array of high speed, infrared detectors. Temperature fields were measured for cracks growing at speeds from 700m/s to 1900m/s. Maximum temperature increases were as high as 465°C. The temperature fields were differentiated to determine the plastic work rate distribution at the crack tip and to estimate the plastic strain rate. Effects of crack tip heating on dynamic fracture toughness are discussed.
Three Dimensional Effects in Interfacial Crack Growth
Authors: Liechti K. M. , Chai Y.-S.
Published: April 2009

An increase of interfacial toughness, associated with increases in in-plane or antiplane shear components, has been noted for a number of bimaterial combinations. Some recent results are reviewed which suggest that the toughening effect could not be completely accounted for by plastic dissipation, bulk viscoelastic dissipation or asperity shielding. The possibility of changes in crack front shape under various loading directions is therefore considered.
Failure of Brittle Adhesive Joints
Authors: Suo Z.
Published: April 2009

Several mechanics problems of brittle adhesive joints are discussed in the light of recent calculations, including issues in fracture testing, concept of nominal toughness, configurational stability of mode-I in-layer fracture, tunnel crack and parallel debond due to residual stresses.
Prediction of Energy Release Rate for Mixed-Mode Delamination Using Classical Plate Theory
Authors: Schapery R. A. , Davidson B. D.
Published: April 2009

Prediction of the energy release rate (ERR) and its components for mixed-mode delamination of composite laminates is discussed. A classical plate theory (CPT) version of Irwin’s virtual crack closure method is developed and used for the ERR, first for plane strain and then for three-dimensional deformations. It is shown that CPT does not provide quite enough information to obtain a decomposition of ERR into its opening and shearing mode components. Results from a continuum analysis are needed to complete the decomposition; but analysis of only one loading case is required for two-dimensional and certain three-dimensional problems. In two example problems the finite element method is used with CPT to complete the mode decomposition. Results from CPT and the finite element method are then compared for several cases.
Probabilistic Perspective on the Failure of Composite Laminae
Authors: Duva J. M. , Lang E. J. , Mirzadeh F. , Herakovich C. T.
Published: April 2009

A probabilistic approach is presented for predicting the applied stress at failure for notched and unnotched unidirectional brittle matrix fibrous composites. It is assumed that failure is caused by the transverse normal stress alone. The mean value of the applied stress at failure can be calculated for any test coupon once the distribution of the transverse normal stress is known. Results are presented for axial and transverse tensile loading of notched coupons and transverse tensile loading of unnotched coupons. The widely observed linear ln–ln relationship between applied stress at failure and notch size is predicted.
Thermal Residual Stress in a Two-Dimensional In-Plane Misoriented Short Fiber Composite
Authors: Taya M. , Dunn M. , Derby B. , Walker J.
Published: April 2009

Residual stress induced in a misoriented short fiber composite due to thermal expansion mismatch between the matrix and fiber is investigated. The case of two-dimensional in-plane fiber misorientation is considered. The elastic model that is developed is based on Eshelby’s equivalent inclusion method and is unique in that it accounts for interactions among fibers at different orientations. A parametric study is performed to demonstrate the effects of fiber volume fraction, fiber aspect ratio, fiber distribution cut-off angle, and fiber distribution type on thermal residual stress. Fiber volume fraction and aspect ratio are shown to have more significant effects on the magnitude of the thermal residual stresses than the fiber distribution type and cut-off angle.
Progressive Failure of Laminated Composites Containing a Hole
Authors: Lessard L. B. , Chang K. Y. , Chang F. K.
Published: April 2009

Failure of laminated composites containing holes and subjected to tension or compression was studied. The major focus was to understand the failure mechanisms of composites induced by stress concentrations, and to determine the effects of ply orientation and geometry on the damage progression of the composites as a function of the applied load. A progressive failure analysis was developed which contained a stress analysis for calculating the stresses inside the materials at a given load and a failure analysis for assessing damage and the mode of failure as a function of the applied load. Tests were performed to evaluate the validity of the analysis. Some tests were stopped at a fraction of the total failure load, and X-radiographs were taken to evaluate the extent of damage and mode of failure. The predictions agreed favorably with the experimental results.
Modeling Temperature and Strain Rate Dependent Large Deformations of Metals
Authors: Bammann Douglas J.
Published: April 2009

We review the development of a strain rate and temperature dependent plasticity model for finite deformation. In particular we address both the method of determining the parameters of the model and the engineering meaning of the parameters in terms of uniaxial stress-strain curves. The ability of the model to predict some aspects of anisotropic hardening, strain rate history effects, and thermal softening are then illustrated by comparison with experimental data.
Steady-State and Transient Zener Parameters in Viscoplasticity: Drag Strength Versus Yield Strength
Authors: Freed A. D. , Walker K. P.
Published: April 2009

A hypothesis is put forth which enables the viscoplastician to formulate a theory of viscoplasticity that reduces, in closed form, to the classical theory of creep. This hypothesis is applied to a variety of drag and yield strength models. Because of two theoretical restrictions that are a consequence of this hypothesis, three different yield strength models and one drag strength model are shown to be theoretically admissible. One of these yield strength models is selected as being the most appropriate representation for isotropic hardening.
Experimental Basis for Temperature-Dependent Viscoplastic Constitutive Equations
Authors: Lindholm U. S.
Published: April 2009

In this paper the author reviews experimental data which is felt to be illustrative of time-dependent, high temperature deformation of metals and, therefore, instructive for the development of constitutive models. Issues addressed are the interrelation between time (strain rate) and temperature, the development of evolutionary equations for both isotropic and directional hardening and recovery, and the orientation of the inelastic strain rate with respect to stress during nonproportional loading.
Anisotropic Constitutive Modeling of a Single Crystal Superalloy at Elevated Temperature
Authors: Stouffer D. C. , Sheh M. Y. , Dame L. T.
Published: April 2009

An anisotropic constitutive model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables in the inelastic flow equation for slip in each slip system. Experiments were conducted to evaluate the need of back stress in the model. The test results showed the effect of reverse inelastic flow on unloading is orientation dependent, and that a back stress state variable in the inelastic flow equation is necessary for predicting the anelastic behavior. Model correlations and predictions with experimental data are presented for the single crystal superalloy Rene’ N4 at 760C and 982C.
Design and Analysis of Finite Element Methods for the Helmholtz Equation in Exterior Domains
Authors: Harari Isaac , Hughes Thomas J. R.
Published: April 2009

Finite element methods for the reduced wave equation in unbounded domains are presented. A computational problem over a finite domain is formulated by imposing an exact impedance relation at an artificial exterior boundary. Method design is based on a detailed examination of discrete errors in simplified settings, leading to a thorough analytical understanding of method performance. For this purpose, model problems of radiation with inhomogeneous Neumann boundary conditions, including the effects of a moving acoustic medium, are considered for the entire range of propagation and decay. A Galerkin/least-squares method is shown to exhibit superior behavior for this class of problems.
Fluid-Structure Interaction in Underwater Acoustics
Authors: Oden J. T. , Demkowicz L. , Bennighof J.
Published: April 2009

A short review of an ongoing work on linear acoustics problems in TICOM is presented.
Directional Solidification
Authors: Davis Stephen H.
Published: April 2009

The mechanical and electrical properties of crystals produced by a unidirectional process depend strongly on the temperature and flow field in the melt since these control the concentration of solute at the melt–crystal interface. The solute gradient there drives morphological instabilities that lead to cellular or dendritic interfaces. This paper discusses the planar–cellular transition and the description of cellular phenomena in theoretical terms.
Oscillatory Instabilities in Cellular Solidification
Authors: Brattkus K.
Published: April 2009

We adapt the recent derivation of a long-wave evolution equation for a solid-liquid interface undergoing directional solidification near the limit of absolute stability to the case of a symmetric model that includes solid diffusion. The stability of steady and spatially periodic solutions are investigated and it is found that these cellular solutions are subject to an oscillatory instability with twice the wavenumber of the underlying pattern. We discuss this instability in the context of experiments on the directional solidification of nematic liquid crystals.
Structure of a Convecting Mushy Layer
Authors: Worster M. Grae
Published: April 2009

Steady, compositional convection in a mushy layer, cooled from below, is analysed for cases in which the Rayleigh number is very large. Solutions are found in which the flow is downwards everywhere except through narrow, vertical chimneys in the layer. The fluxes of mass, heat and solute from the mushy layer into the overlying melt are determined in terms of a single parameter that is proportional to the number density of chimneys. The model solutions can be used to interpret the results of laboratory experiments.
Interface Instabilities During Laser Melting of Thin Films
Authors: McFadden G. B. , Coriell S. R. , Brush L. N. , Jackson K. A.
Published: April 2009

Thin silicon films on a cooled substrate are often found to develop two-phase lamellar structures upon radiative heating. Jackson and Kurtz developed a two-dimensional model for the process in which the heated film consists of alternating parallel bands of liquid and solid phases separated by straight solid-liquid interfaces. To understand the cellular or dendritic structures that sometimes are observed in these interfaces, they also performed a linearized morphological stability analysis and obtained the conditions for the growth or decay of infinitesimal perturbations to the interface. In this work we extend that analysis to finite amplitudes by developing a boundary integral representation of the thermal field, and obtain numerical solutions for nonplanar solid-liquid interfaces.
Kinetic Effects in Directional Solidification
Authors: Merchant G. J. , Davis S. H.
Published: April 2009

Mullins and Sekerka showed for fixed temperature gradient that the planar interface is linearly stable for all pulling speeds V above some critical value, the absolute stability limit. Near this limit, where solidification rates are rapid, the assumption of local equilibrium at the interface may be violated. We incorporate nonequilibrium effects into a linear stability analysis of the planar front by allowing the segregation coefficient and interface temperature to depend on V in a thermodynamically-consistent way. In addition to the steady cellular mode, we find a new branch of long-wavelength time-periodic states. Under certain conditions there exists a stability window separating the steady and oscillatory branches.
Airway Closure at Low Lung Volume: The Role of Liquid Film Instabilities
Authors: Kamm R. D. , Johnson M.
Published: April 2009

A model is presented to study the hypothesis that closure of pulmonary airways occurs as a result of an instability of the liquid layer lining the airway walls. Recent experimental results are reviewed that lead to predictions of closure, based on statically stable configurations, in the terminal bronchioles of the lung when lung volumes fall to about 20% of maximal lung volume. An approximate numerical model is developed to examine the dynamic process, simulating the collapse of the liquid film as airway volume falls during an expiration. Results are used to determine under what conditions the time-scale for film collapse is significant compared to typical expiration times.
Response of Arteries to Near-Wall Fluid Dynamic Behavior
Authors: Giddens D. P. , Zarins C. K. , Glagov S.
Published: April 2009

Arteries are living tissues which react and adapt to their environment, particularly in relation to changes in the rate of blood flow required to supply peripheral tissues or organs. Medium and small size arteries increase in diameter in response to short-term demands for increased flow and decrease in diameter in the event of diminished demands. Such immediate reactions are regulated primarily by vasoactive substances acting directly on smooth muscle cells of the media or by release of smooth muscle relaxation or contraction factors elaborated by endothelial cells. Chronic or long-term changes in arterial diameter appear to be governed directly by near-wall flow phenomena, e.g. the fluid dynamic wall shear. Recent evidence suggests that the normal tendency of arteries to respond to long-term changes in the shear field can result in intimal thickening and that this response may also favor the development of atherosclerosis. Thus, there appears to be a close relationship between fluid dynamics and the structure of arteries. From the fluid dynamics viewpoint, the pulsatile, three dimensional nature of blood flow requires sophisticated experimental methods in order to provide adequate data for correlation with biological studies. Research within the past decade has led to the conclusion that arteries seek a vessel diameter-blood flow combination which results in a flow-induced mean wall shear stress of approximately 15 dynes/sq.cm. If this value is chronically exceeded, vessel enlargement develops. If normal baseline shear stress is not restored by this increase in radius, the local response may continue. Conversely, reduced wall shear tends to induce intimal thickening in order to reduce lumen radius and thus increase wall shear toward normal levels. Under certain conditions this reaction may progress to the development of atherosclerotic plaques. Despite this knowledge, key points remain to be clarified. Is it the wall shear stress or the wall shear rate which determines the reaction? The former possibility implies that a mechanical shear-related stimulus is at the heart of the biological response mechanisms while the latter suggests a mass transport-related mechanism.
High Strain Rate Behavior of Metals
Authors: Clifton R. J.
Published: April 2009

Experimental results on the high strain rate response of polycrystalline metals are reviewed, with emphasis on the behavior of pure metals. A strong increase in flow stress with increasing strain rate is reported for strain rates of approximately 105s−1 and higher. This increase is observed in pressure-shear plate impact experiments at nominally constant strain rates from 105s−1 to 106s−1. To improve understanding of the increased rate sensitivity at high strain rates, pressure-shear, strain-rate-change experiments have been conducted on OFHC copper specimens. These experiments have been analyzed using a conventional viscoplasticity formulation and an internal variable formulation in which the hardening rate depends on the rate of deformation. Only the latter formulation is successful in describing the observed response to the change in strain rate. This observation is discussed in terms of its implications for interpreting other dynamic plasticity experiments and for improved understanding of the underlying dislocation mechanisms. The enhanced rate sensitivity at high strain rates is concluded to be related primarily to the rate sensitivity of strain hardening, not the rate sensitivity of the flow stress at constant structure.
Panel Method Control in 3-D Hyberbolic Grid Generation
Authors: Hounjet M. H. L.
Published: April 2009

A method is presented for the generation of OH type grids about transport type aircraft. The method combines a hyperbolic grid generation scheme with source terms obtained with a panel method in such a way that OH type grids around fairly complex shapes with concavities can be generated easily. The components of the method: a method to generate grids with a panel method and the hyperbolic grid generation scheme, will be described and applications will be shown.
Knowledge-Based Nonlinear Boundary Integral Models of Compressible Viscous Flows Over Arbitrary Bodies: Taking CFD Back to Basics
Authors: Hunt Barry
Published: April 2009

The paper starts with a discussion of a knowledge-based CFD methodology. A new incompressible formulation known as SAVER is first introduced, employing a novel relaxation approach. This is then generalized through a modification of the boundary conditions to the GENESIS methodology, for analysis or design in compressible, rotational flow. A discussion is presented of how the basic causal nature of integral methods offers new insights into certain flow phenomena, such as shocks and separations, and facilitates aerodynamic sensitivity analysis. The paper presents a new class of vector fields approximating the Euler equations for transonic flows, and shows how GENESIS can be used to construct first an exact solution of these approximate fields, then a numerical solution of the residual error fields. The explicit representation of a shock discontinuity on the body boundary exploits its causal link with conditions at the sonic point to suppress, non-dissipatively, the mathematically-valid but physically-impossible formation of an expansion shock.
Spheroidal Sliding Inclusion in an Elastic Half-Space
Authors: Jasiuk Iwona , Tsuchida Eiichiro , Mura Toshio
Published: April 2009

An analytical elasticity solution for a half-space having a spheroidal sliding inclusion is obtained. The inclusion is subjected to either a uniform plane hydrostatic loading applied at infinity or a uniform transformation strain (eigenstrain). The interface between the inclusion and the surrounding material allows sliding and does not sustain shear tractions. Boussinesq’s displacement potentials in infinite integral form and in infinite series form are used in the analysis. Numerical examples are included.
Shear Deformation and Buckling of Columns
Authors: Kelly J. M.
Published: April 2009

It is shown that the prediction of buckling loads of columns that are very weak in shear is crucially dependent on the choice of direction for the axial load of the column in the buckled configuration. Examples are given showing the wide differences in buckling load predicted by different choices. The results are applicable to columns of sandwich construction, springs, and multilayer elastomeric bearings for isolation systems.
Mode III Fracture Mechanics Analysis With Fourier Series Method
Authors: Kwok F. W. M. , Kang L. C. , Steele C. R.
Published: April 2009

A numerical scheme based on the Fourier series method is developed for the solution of Laplace’s equation on a polygonal domain. This scheme is applied to the solution of the pure mode III fracture mechanics problem. For the single edge cracked strip problem under out-of-plane loading, the value of the J-Integral evaluated from the Fourier solution was found to be in good agreement with classical solution. The real power of the scheme lies in its applicability to general polygonal shapes. This capability is illustrated by three sample problems that involve strips with a slanted crack, multiple cracks and branching cracks under mode III loading.
Analytical and Experimental Investigation on a Vibrating Timoshenko Beam Clamped at One End and Carrying a Finite Mass at the Other
Authors: Laura P. A. A. , Rossi R. E. , Ercoli L. , La Malfa S.
Published: April 2009

An exact solution of the title problem is presented. Experimental results are obtained and it is shown that they are in reasonably good agreement with the analytical predictions.
Behavior of Thin-Walled Beams Made of Advanced Composite Materials and Incorporating Non-Classical Effects
Authors: Librescu Liviu , Song Ohseop
Published: April 2009

Several results concerning the refined theory of thin-walled beams of arbitrary closed cross-section incorporating non-classical effects are presented. These effects are related both with the exotic properties characterizing the advanced composite material structures and the non-uniform torsional model. A special case of the general equations is used to study several problems of cantilevered thin-walled beams and to assess the influence of the incorporated effects. The results presented in this paper could be useful towards a more rational design of aeronautical or aerospace constructions, as well as of helicopter or tilt rotor blades constructed of advanced composite materials.
Geometric Elements in the Elastic-Plastic Analysis of a Cylindrical Shell
Authors: Lukasiewicz S. , Nowinka J.
Published: April 2009

The paper deals with an elastic-plastic analysis of a cantilever cylindrical shell loaded at its free end by a concentrated radial force. The problem is solved by means of the so-called “geometric elements” which conform to the deformation pattern of the shell. The results obtained define the large deformation behavior and the motion of plastic zones over the surface of the shell. A comparison with a standard finite element solution is made, and the advantages of the geometric approach are shown.
Instability of Discrete Pseudo-Conservative Structural Systems
Authors: Mirasso Anibal E. , Godoy Luis A.
Published: April 2009

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.
Transient Waves in a Class of Random Heterogeneous Media
Authors: Ostoja-Starzewski Martin
Published: April 2009

A stochastic method is developed for analysis of transient waves propagating in one-dimensional random granular-type media. The method is suited to study transient dynamic response of nonlinear microstructures with material randomess, of high signal-to-noise ratio, being present in constitutive moduli and grain lengths. It generalizes the classical solution techniques, based on the theory of characteristics, by taking advantage of the Markov property of the forward propagaing disturbances. Pulses propagating in bilinear elastic, nonlinear elastic, and linear-hysteretic media are studied. Additionally, a short review is given of an investigation of acceleration wavefronts making a transition into shocks in random nonlinear elastic/dissipative continua, where Markov property can again be exploited.
Signal Processing Techniques for Nonlinear Structural Dynamical Systems
Authors: Pezeshki C. , Miles W. H. , Elgar S.
Published: April 2009

Various signal processing techniques are introduced into the structural dynamics literature, notably higher-order spectra for steady-state response and wavelet transforms for transient response of systems. The structural behavior of the buckled beam, modeled by the one-mode Galerkin approximation is examined to demonstrate the utility of the techniques. Higher-order spectra illuminate nonlinear energy coupling mechanisms in the frequency domain for the steady state response. Wavelet transforms show the development of the frequency spectrum in the transient portion of the response.
Minimum Weight Design of Laminated Composite Plates for Postbuckling Performance
Authors: Shin Dong Ku , Gu¨rdal Zafer , Griffin O. Hayden
Published: April 2009

Minimum-weight design of simply-supported, symmetrically laminated, thin, rectangular, specially orthotropic laminated plates for buckling and postbuckling strength is investigated. The postbuckling analysis is based on an Marguerre-type energy method extended to generally orthotropic plates with a special consideration of the mode change in the postbuckling load regime. The failure load of laminates is calculated by the maximum strain failure criterion based on the in-plane strains. Design variables are individual layer thicknesses with specified fiber orientations and assumed to take only discrete values corresponding to multiples of the lamina thickness. The optimization with discrete valued design is achieved by introducing additional penalty terms, in the form of a sine function, to the regular pseudo-objective function of sequential unconstrained minimization technique (SUMT). The proposed optimization technique is applied to the design of rectangular laminates made up of 0, ± 45, 90 degree laminae with various aspect ratios loaded by axial compressive loads.
Impact Response of Fiber Composite Structures
Authors: Swanson Stephen R.
Published: April 2009

The problem of impact loading of fiber composite structures is important because of the possibility of accidental damage occuring during service. The present paper is a review of a combined experimental and analytical study of transverse impact loading of carbon/epoxy composite plates and cylinders. Scaling of response with structure size was investigated as part of the program. Analysis procedures for dynamic response were developed, using Ritz techniques for plates and Fourier series expansions combined with Laplace transforms for the cylinders. The experimental results showed good correlation with scaling rules developed for structural response. Good agreement was also obtained between experiment and analysis for surface strain response in both the plates and the cylinders. Scaling of damage is seen to be more complicated, with measured delamination sizes exhibiting a dependence on absolute specimen size as would be predicted by fracture mechanics.
Dynamics of Cracked Rotating Blades
Authors: Wauer Jo¨rg
Published: April 2009

The modeling and formulation of equations of motion for a cracked rotating blade are studied. The proposed model is a Bernoulli-Euler beam with a single transverse crack. Two fields are connected by a local spring element characterizing the reduced stiffness of the crack region. First, the governing nonlinear boundary value problem is derived. Next, the stationary deformation state is dealt with. Finally, the linearized equations of motion for small superimposed oscillations are formulated. The paper corresponds with another one of the same author on cracked rotating shafts and shows that several essential modifications are necessary.
Separated Solution Procedure for Bending of Circular Plates With Circular Holes
Authors: Bird M. D. , Steele C. R.
Published: April 2009

A separated solution procedure is presented for the two-dimensional bi-harmonic equation on circular domains with circular holes and arbitrary boundary conditions. The solutions use the traditional trigonometric Fourier series on the boundaries with a power series decay into the domain. The interaction of the boundaries is expressed simply and exactly resulting in quick processing time. The only simplification made is the use of a finite number of terms in the boundary conditions.
Integral Equation Methods for Linear and Nonlinear Aerodynamics
Authors: Yates E. Carson
Published: April 2009

This paper reviews the NASA Langley Research Center program for development of integral-equation aerodynamic methods with emphasis on application in computed-aided multidisciplinary design processes as well as in aerodynamic design and stand-alone analysis. The accomplishments, status, and outlook of the program are discussed in order to highlight the scope, generality, versatility, and attractive features of this methodology, especially for application to nonlinear problems.
Identification of Nonlinearity in Structural Systems: Theory, Simulation, and Experiment
Authors: Zavodney L. D.
Published: April 2009

A procedure to identify nonlinear structural systems caused by quadratic or cubic stiffness nonlinearity, geometric asymmetry, internal resonance, and subject to parametric excitation is proposed. The method uses conventional instrumentation and modal analysis techniques to match observed behavior in the structural response to the behavior of nonlinear analytical models when subject to random, impulse, or harmonic excitations. Some of the structures studied in this paper behave linearly when subject to one type of excitation but exhibit uniquely nonlinear behavior when subject to other types of excitation.
Small Strain and Moderate Rotation Theory in Elasticity and Stability
Authors: Altman Wolf , Bevilacqua Luiz
Published: April 2009

This paper is concerned with a small strain and moderate rotation theory in elasticity and stability. Approximate kinematic relations and associated equations of motion are obtained, based on estimates of the displacement gradient components. Stability equations are derived with several levels of approximation from the equations of motion and boundary conditions. A version of the basic equations referred to a local orthogonal coordinate system is written in terms of physical components.
Experimental Determination of the Elongational Viscosity of Polymer Solutions
Authors: Chavez A. E. , Manero O. , Bao H. Y. , Gupta R. K.
Published: April 2009

A comparative study is performed between elongational flow data obtained from fiber spinning and a numerical scheme based on the expressions derived from an anisotropic FENE dumbbell model, with conformation-dependent hydrodynamic friction, coupled with a differential momentum balance made along the spinning filament. Extensional flow data was obtained by using the Gupta-Sridhar extensional viscometer. The test fluid was an aqueous solution of a copolymer of sodium acrylate and acrylamide (Alcomer 120). From the information obtained by this comparison, we assess the influence of preshearing and other factors on the rheological behavior of polymer solutions using this technique.
Equations for Nonlinear Analysis of 3D Motions of Beams
Authors: Crespo da Silva M. R. M.
Published: April 2009

The formulation of a set of mathematically consistent differential equations for analyzing nonlinear flexural–flexural–torsional–extensional motions of an Euler–Bernoulli beam is presented. The beam may be mounted on a rotating or on a non–rotating base. A brief discussion on an Euler-like form of the equations is also presented. When the equations are expanded about their equilibrium solution to a desired order in an artificial “bookkeeping parameter” ε, the resulting equations are well suited for a perturbation analysis of the motion. Such analysis discloses a number of important nonlinear phenomena exhibited by the system. Order ε3 equations expanded about the zero equilibrium are also developed here.
Photoelastic Study of Friction
Authors: Dally James W. , Chen Yung-Mien
Published: April 2009

A new method of measuring the normal and sliding loads associated with multiple point contact is introduced. A multiple point contact is modeled with a steel die with a profile that simulates a rough surface. A very large scale factor is used in modeling this surface. The steel die is placed in contact with a photoelastic model of a half plane and is subjected to a normal load. This normal load is partitioned over the multiple points of contact producing an isochromatic fringe pattern that describes the stress distribution in the local neighborhood of the contact points. A sliding load is then imposed on the model which destroys the symmetry of this fringe pattern. The fringe data in this pattern is sufficient to determine the local loads Pi and Qi and the local coefficient of friction fi = Qi / Pi at each contact point. An overdeterministic method is introduced which gives the solution for Pi, Qi and fi using many data points taken from the isochromatic pattern in the local neighborhood of the contacts.
Integral Equations Obtained From the Probabilistic Strength of Bars Subjected to Pure Torsion
Authors: Di´az G. , Marti´nez V. , Kittl P.
Published: April 2009

The present work is a collection of results relating to the application of the integral equations method to the case of prismatic bars subjected to pure torsion. The specific risk of fracture functions are independently obtained for volume and surface brittlenesses, and when the material of the bar simultaneously exhibits the two types of brittleness, both can be separated. In the cases of a square bar and a bar having a regular polygon cross section of n sides, a simple stress field is used. The particular cases of equilateral triangle, square, and circular cross section are explicitly indicated in the formulas. On the other hand, the cases of a round, a rectangular, and an elliptical bar are treated, knowing exactly the stress field acting in the bar’s cross section. The particular cases of a square, a thin rectangular, and a round bar are also studied. The purpose of this review is to emphasize that the specific risk of fracture function can be obtained without knowing previously its analytical form by solving an integral equation.
Resonant Frequency Calculations Using a Hybrid Perturbation-Galerkin Technique
Authors: Geer James F. , Andersen Carl M.
Published: April 2009

A two step hybrid perturbation-Galerkin technique is applied to the problem of determining the resonant frequencies of one- or several-degree(s)-of-freedom nonlinear systems involving a parameter. In step one, the Lindstedt-Poincare´ method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g. for small or large values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in a Galerkin type approximation. The technique is illustrated for several one-degree-of-freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.
Eigenvalue Problem for Uncertain Systems
Authors: Grigoriu Mircea
Published: April 2009

Methods are developed for calculating probabilistic characteristics of the eigenvalues of stochastic symmetric matrices. The methods are based on the relationship between the elements of a matrix and its eigenvalues, perturbation method, bounds on eigenvalues, and zero-crossings of the characteristic polynomial. It is shown that the polynomial characteristic of a stochastic matrix can be viewed as a random process whose crossings of level zero define the eigenvalues of the matrix. The proposed methods of analysis are demonstrated by examples from dynamics and elasticity.
Optimal Design of Viscoelastically Damped Beam Structures
Authors: Hajela P. , Lin C.-Y.
Published: April 2009

Enhancement of damping characteristics of beam structures via application of viscoelastic damping material is formulated as a multicriterion optimization problem. The design space for the problem consists of a mix of continuous, discrete, and integer design variables. Two distinct approaches, one a variant of the global criterion approach, and the other a specialized implementation of the genetic search method, are proposed as alternative solutions to this problem. While the first approach belongs to the general category of nonlinear programming methods, the genetic search strategy has its basis in stochastic search, and offers some distinct advantages in the problem under consideration. Results obtained in this work clearly demonstrate the relative importance of structural weight and desired modal damping on how the damping material must be applied to the beam.
On the Effect of Anisotropy and Inertia on Shear Banding: Instability of Biaxial Stretching
Authors: Zhu H. , Zbib H. M. , Aifantis E. C.
Published: April 2009

The instability of biaxial stretching leading to the development of shear bands in viscoplastic materials with both isotropic hardening and kinematic hardening is examined. The main issues are to evaluate the effect of anisotropy and inertia on the onset of instability and to examine the development and evolution of an inhomogeneous deformation structure, using both a linear analysis and a nonlinear finite element analysis. It is shown that the back stress and plastic spin, modeling deformation induced anisotropy and texture development, have a significant influence on the critical state at which the first instability occurs. The corotational rate of the back stress and its relation to the spin of the substructure produces apparant softening, causing instability at positive strain hardening (in the absence of back stress and corotational rates instability occurs at zero hardening). When decreasing the magnitude of the spin of the substructure by varying the plastic spin parameter the critical value of the hardening parameter decreases towards zero, illustrating again the softening effect of the spin. It is also shown that at the onset of instability, the linear analysis predicts the development of a periodic structure of square cells, implying that although the deformation has become inhomogeneous it is far from being localized. The nonlinear finite element analysis also predicts the formation of a square cell pattern at the onset of instability. This pattern however evolves into localized shear bands far into the post localization regime as shown by the nonlinear analysis.
The Structure of Shear Bands in Idealized Granular Materials
Authors: Bardet J. P. , Proubet J.
Published: April 2009

The structure of shear bands in granular materials was investigated by numerically simulating an idealized assembly of two-dimensional particles. Flexible stress-controlled boundaries were used instead of periodic boundaries to avoid constraining the motion of particles within the tested specimen. The particle displacement, particle rotations and rotations of the particle neighborhoods (macro-rotation) were examined within the shear band. The shear band width was found to decrease with axial strain from 18 and 15 times the average particle radius. The particle rotations and macro-rotations were concentrated inside the shear bands. The numerical simulations suggest that the particle rotations are induced by macro-rotations, and support the use of the micropolar theory for examining instable phenomena within granular materials.
Analysis of Shear Bands in Simple Shearing Deformations of Nonpolar and Dipolar Viscoplastic Materials
Authors: Batra R. C.
Published: April 2009

During the past few years we have studied numerically the initiation and growth of shear bands in nonpolar and dipolar viscoplastic materials being deformed in simple shear, and in nonpolar materials undergoing plane strain deformations. We summarize here our work for the former problem.