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NASA NTRS1992

Fiber shape effects on metal matrix composite behavior

The effects of different fiber shapes on the behavior of a SiC/Ti-15 metal matrix composite is computationally simulated. A three-dimensional finite element model consisting of a group of nine unidirectional fibers is used in the analysis. The model is employed to represent five different fiber shapes: a circle, an ellipse, a kidney, and two different cross shapes. The distribution of microstresses and the composite material properties, such as moduli, coefficients of thermal expansion, and Poisson's ratios, are obtained from the finite element analysis for the various fiber shapes. Comparisons of these results are used to determine the sensitivity of the composite behavior to the different fiber shapes and assess their potential benefits. No clear benefits result from different fiber shapes though there are some increases/decreases in isolated properties.

Brown, H. C.↗

NASA NTRS1987

Calculation of stresses and forces between the skin and stiffener in composite panels

A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and on elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress function. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. The local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.

Hyer, M. W.↗

NASA NTRS1986

A finite element approach for solution of the 3D Euler equations

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Thornton, E. A.↗

NASA NTRS1994

Scattering Cross Section of Sound Waves by the Modal Element Method

#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.

Baumeister, Kenneth J.↗

NASA NTRS1992

Fiber shape effects on metal matrix composite behavior

The effects of different fiber shapes on the behavior of metal matrix composites is computationally simulated. A three-dimensional finite element model consisting of a group of nine unidirectional fibers in a three by three unit cell array of a SiC/Ti-15-3 metal matrix composite is used in the analysis. The model is employed to represent five fiber shapes that include a circle, an ellipse, a kidney, and two different cross shapes. The distribution of stresses and the composite material properties, such as moduli, coefficients of thermal expansion, and Poisson's ratios, are obtained from the finite element analysis using the various fiber shapes. Comparisons of these results are used to determine the sensitivity of the composite behavior to the different fiber shapes. In general, fiber dominated properties are not affected by fiber geometry and matrix dominated properties are only moderately affected.

Brown, H. C.↗

NASA NTRS1994

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Baumeister, Kenneth J.↗

NASA NTRS1990

A finite element conjugate gradient FFT method for scattering

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Collins, Jeffery D.↗

NASA NTRS1984

A spectral element method for fluid dynamics - Laminar flow in a channel expansion

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

Patera, A. T.↗

NASA NTRS1990

Large scale nonlinear numerical optimal control for finite element models of flexible structures

This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.

Shoemaker, Christine A.↗

NASA NTRS1981

Static shape determination and control for a large space antenna

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and quadratic performance criteria for the comparison of estimates or control forces. Results are illustrated by simulations with a finite element model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic model. These expansions provide approximate solutions in the event that a closed form analytical solution to the system boundary value problem is not available.

Weeks, C.↗

NASA NTRS1993

An augmented Young-Laplace model of an evaporating meniscus in a micro-channel with high heat flux

High flux evaporations from a steady meniscus formed in a 2 micron channel is modeled using the augmented Young-Laplace equation. The heat flux is found to be a function of the long range van der Waals dispersion force which represents interfacial conditions between heptane and various substrates. Heat fluxes of (1.3-1.6) x 10(exp 6) W/m(exp 2) based on the width of the channel are obtained for heptane completely wetting the substrate at 100 C. Small channels are used to obtain these large fluxes. Even though the real contact angle is 0 deg, the apparent contact angle is found to vary between 24.8 deg and 25.6 deg. The apparent contact angle, which represents viscous losses near the contact line, has a large effect on the heat flow rate because of its effect on capillary suction and the area of the meniscus. The interfacial heat flux is modeled using kinetic theory for the evaporation rate. The superheated state depends on the temperature and the pressure of the liquid phase. The liquid pressure differs from the pressure of the vapor phase due to capillarity and long range van der Waals dispersion forces which are relevant in the ultra think film formed at the leading edge of the meniscus. Important pressure gradients in the thin film cause a substantial apparent contact angle for a complete wetting system. The temperature of the liquid is related to the evaporation rate and to the substrate temperature through the steady heat conduction equation. Conduction in the liquid phase is calculated using finite element analysis except in the vicinity of the thin film. A lubrication theory solution for the thin film is combined with the finite element analysis by the method of matched asymptotic expansions.

Wayner, P. C., Jr.↗

NASA NTRS1979

Rail shear test method

The results of both an experimental test program and a finite element analysis of selected graphite/polyimide rail shear test specimens are discussed. The two dimensional finite element analysis includes both mechanical and thermal loading (differential expansion) of the specimens and their elastic rails. Parameters in this analysis of unidirectional and symmetric, balanced angle-ply laminates include ply layup angles, the effect of flexible rails, the method of load introduction to the specimen and the effect of uniform heating of the specimen and rails. Two types of tensile rail shear fixtures were investigated experimentally: a uniform thickness, bolted-rail shear fixture loaded diagonally across the specimen test section; and a tapered thickness, bonded-rail shear fixture loaded axially along the center-line of the specimen test section. Test results include room-temperature and 589K strain data taken from the center of the specimen test section during loading.

Garcia, R.↗

NASA NTRS1983

Characteristics of thermally-induced transverse cracks in graphite epoxy composite laminates

The characteristics of thermally induced transverse cracks in T300/5208 graphite-epoxy cross-ply and quasi-isotropic laminates were investigated both experimentally and analytically. The formation of transverse cracks and the subsequent crack spacing present during cool down to -250 F (116K) and thermal cycling between 250 and -250 F (116 and 394K) was investigated. The state of stress in the vicinity of a transverse crack and the influence of transverse cracking on the laminate coefficient of thermal expansion (CTE) was predicted using a generalized plane strain finite element analysis and a modified shear lag analysis. A majority of the cross-ply laminates experienced transverse cracking during the initial cool down to -250 F whereas the quasi-isotropic laminates remained uncracked. The in situ transverse strength of the 90 degree layers was more than 1.9 times greater than the transverse strength of the unidirectional 90 degree material for all laminates investigated.

Adams, D. S.↗

NASA NTRS1992

Modal element method for scattering of sound by absorbing bodies

The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Baumeister, Kenneth J.↗

NASA NTRS1993

Modal element method for scattering and absorbing of sound by two-dimensional bodies

The modal element method for acoustic scattering from a 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Baumeister, K. J.↗

NASA NTRS2009

Analytical Predictions of Thermal Stress in the Stardust PICA Heatshield Under Reentry Flight Conditions

We performed finite element analyses on a model of the Phenolic Impregnated Carbon Ablator (PICA) heatshield from the Stardust sample return capsule (SRC) to predict the thermal stresses in the PICA material during reentry. The heatshield on the Stardust SRC was a 0.83 m sphere cone, fabricated from a single piece of 5.82 cm-thick PICA. The heatshield performed successfully during Earth reentry of the SRC in January 2006. Material response analyses of the full, axisymmetric PICA heatshield were run using the Two-Dimensional Implicit Ablation, Pyrolysis, and Thermal Response Program (TITAN). Peak surface temperatures were predicted to be 3385K, while the temperature at the PICA backface remained at the estimated initial cold-soak temperature of 278K. Surface recession and temperature distribution results from TITAN, at several points in the reentry trajectory, were mapped onto an axisymmetric finite element model of the heatshield. We used the finite element model to predict the thermal stresses in the PICA from differential thermal expansion. The predicted peak compressive stress in the PICA heatshield was 1.38 MPa. Although this level of stress exceeded the chosen design limit for compressive stresses in PICA tiles for the design of the Orion crew exploration vehicle heatshield, the Stardust heatshield exhibited no obvious mechanical failures from thermal stress. The analyses of the Stardust heatshield were used to assess and adjust the level of conservatism in the finite element analyses in support of the Orion heatshield design.

Squire, Thomas↗

NASA NTRS1981

On the relationship between engineering properties and delamination of composite laminates

The influence of the coefficient of mutal influence, Poisson's ratio and coefficients of thermal and moisture expansion on delamination is studied. Engineering theories are compared to finite element and experimental results. It is shown that the mismatch in coefficients of mutual influence can have a strong influence on delamination with fiber angles in the 10-15 degree range being critical for adjacent layer combinations. The mismatch in coefficient of mutual influence is reduced by a factor of two and the interlaminar shear stress is reduced significantly when the + or - adjacent layers are interspersed between 0 and 90 degree layers. It is shown how the results can be used for design of composite laminates.

Herakovich, C. T.↗

NASA NTRS1993

Nonlinear response of graphite-epoxy wide columns subject to eccentric load

It is shown that including the effects of bend-twist coupling and material nonlinearity on the large displacement flexural response of graphite-epoxy wide columns is necessary to adequately model their response. Results from static tests on 0(30)T and (30/0/-30 sub 5)s laminated specimens under eccentric axial compression are compared to a nonlinear analysis. The analysis is based on a Kantrovich expansion of the displacements in the width coordinate and a finite element representation in the axial coordinate. An incremental, updated Lagrangian formulation and element corotational coordinates are employed. Nonlinear elastic material behavior was measured in a separate set of material characterization tests, and these data are used to compute tangent stillnesses in the updated configuration.

Griffin, O. H., Jr.↗