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Structural Mechanics
^ Anisotropic Piezo-Electro-Thermo-Viscoelasticity Theory with Applications to Composites
H. H. Hilton,* J. R. Vinson,* S. Yi* (Nanyang), C. E. Beldica*
University of Illinois; University of Delaware; Nanyang Technological University; National Center for Supercomputing Applications; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

The general, nonlinear, 3-D, large deformation theory of anisotropic piezo-electro-thermoviscoelasticity is formulated and represents the confluence of anisotropic elasticity and thermoviscoelasticity, nonhomogeneous layered media, and piezoelectricity. For linear materials and small deformations, a piezoelastic/piezoviscoelastic analogy is established in terms of integral Fourier and Laplace transforms. To demonstrate the effectiveness of the piezoviscoelastic constitutive relation derivations, several piezoelastic examples of beam and plate solutions have been reformulated in terms of piezoviscoelastic constitutive relations and solved analytically and numerically using viscoelastic finite-element analyses. Researchers are making comparisons with piezoelastic solutions and conducting sensitivity analyses of piezoviscoelastic parameters.

^ Anisotropic Viscoelastic Fractional Derivative Material Characterization
H. H. Hilton*
University of Illinois; National Center for Supercomputing Applications; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of generalized Kelvin models. These are analytically extended to cover general anisotropic viscoelastic behavior. Integral constitutive relations (which are more powerful computationally) are derived from fractional differential ones, and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared, and it is found that use of the former is preferable in analyzing isotropic and anisotropic real materials.

^ Generalized Linear and Nonlinear Viscoelastic Earthquake Motion Simulations
H. H. Hilton,* Y. K. Lin* (Florida Atlantic Univ.)
Florida Atlantic University

The governing relations for nonlinear and linear viscoelastic vertical ground motions caused by an earthquake are formulated. The boundaries of the ratio of vertical to horizontal motion velocity are investigated, and it is shown that they lie in the range from 1.23 to 1.73 for all physical elastic and viscoelastic materials. Numerical simulations indicate that both response displacement and acceleration amplitudes and frequencies are affected by viscoelastic properties of the medium. Since viscoelastic responses are accelerated in time by increases in temperature and moisture content, significant damping effects will be experienced in warm, moist soils.

^ Large Deflections of Linearly Elastic and Viscoelastic Columns with Follower Loads
H. H. Hilton,* S. Yi* (Nanyang), T. Ruijun (Harbin Dongan Engine Co.)
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

A large-deflection analysis of nonhomogeneous linearly elastic or viscoelastic columns with initial curvature and with variable areas subjected to follower loads is formulated. Column end shortening due to both curvature and compressible loads is taken into account, and the governing coupled nonlinear differential equations are solved numerically. The linear elastic-viscoelastic integral transform analogy is analytically extended to this nonlinear problem. The effects of end shortening, follower load angle, nonhomogeneous material properties, and variable area on elastic and viscoelastic columns are studied in detail.

^ Mathematical and Numerical Analysis Issues in Nonlinear Anisotropic Viscoelastic Composites
H. H. Hilton,* S. Yi* (Nanyang), C. E. Beldica*
University of Illinois; Nanyang Technological University; National Center for Supercomputing Applications; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

Complete 3-D anisotropic, nonhomogeneous, large deformation, nonlinear, viscoelastic constitutive relations are formulated including aging, moisture, temperature, degree of cure, and change of state effects. Anisotropic nonlinear heat and temperature relations for cure processes are also studied. The coupled system is solved using combined spatial finite-element and temporal finite-difference and/or fourth-order Runge-Kutta approaches. Stochastic failure criteria are used to determine probabilistic survival times to delamination onset during service and manufacturing conditions. Mesh and incremental time step sizing influences on convergence of numerical results are evaluated, and comparisons of stresses and deformations with experimental data are carried out.

^ Stochastic Delamination Buckling of Viscoelastic Columns
H. H. Hilton,* S. Yi* (Nanyang), C. E. Beldica
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

The effects of random failure criteria on delamination buckling are studied under deterministic loads, geometries, moduli, temperatures, and moisture contents. This allows for an analysis that focuses on and isolates random delamination buckling criteria effects under otherwise deterministic conditions. Viscoelastic failure stresses and moduli decrease in time, while bending stresses, strains, and deformations increase with time. Using the experimentally determined delamination probability distributions reported by Hiel et al. in conjunction with the combined load stochastic failure criterion of Hilton and Ariaratnam, probabilities of delamination onset occurrences as time functions are formulated.

^ Stochastic Viscoelastic Delamination Onset Failure Analysis of Composites
H. H. Hilton,* S. Yi* (Nanyang)
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

The analysis includes stochastic processes due to combined random loads and random delamination failure stresses as well as random anisotropic viscoelastic material properties, including the influence of stochastic temperature fields, moisture contents, and boundary conditions. It is shown that times for delamination onset occurrences in composites can be predicted probabilistically depending on any one or all of the above conditions. For cases where deterministic criteria predict no delamination failures, the present stochastic failure theory indicates high probabilities of failure at either early or long times depending on the load-time relations. The effects of fiber orientation and of number of plies on delamination probabilities are examined.

^ Structural Integrity of Solid Propellants and Filament-Wound Rocket Cases
H. H. Hilton*
University of Illinois; DOE Center for Simulation of Advanced Rockets, 3341494 (ASCF)

Nonlinear analytical and massively parallel numerical analyses of propellants and cases have been initiated. Time-dependent probabilities of failure are determined and finite-element massively parallel protocols are being developed.

^ Nonlinear Thermoviscoelastic Analysis of Interlaminar Stresses in Laminated Composites
S. Yi* (Nanyang), H. H. Hilton,* C. E. Beldica
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

A finite-element formulation for analyzing interlaminar stress fields in nonlinear anisotropic viscoelastic laminated composites is presented, and it includes the hygrothermal formulation. Schapery's single integral formulation is extended to account for anisotropy and multiaxial stress states. Numerical results obtained from the present formulation are compared against experimental data and excellent agreement is obtained between these results. As illustrative examples, inplane and interlaminar stresses for (45/-45)sT300/5208 laminate are also presented.

^ Optimum Material Property Formulation for Anisotropic Viscoelastic Damping
H. H. Hilton,* C. E. Beldica*
University of Illinois; National Center for Supercomputing Applications; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

Anisotropic viscoelastic material properties are formulated analytically taking into account fiber orientations and stacking sequences for laminated composites. The detailed influences of resulting anisotropic moduli are investigated in terms of material response to loads and deformations and the ability to dissipate energy (that is, damp out undesirable motion).

^ Finite-Element Analysis of Coarse-grained Vector Machines of Residual Stresses in Viscoelastic IC Packages during Surface-mounting Processes
S. Yi* (Nanyang), H. H. Hilton*
Nanyang Technological University; University of Illinois

Moisture and temperature distributions and residual stresses in plastic-encapsulated IC packages are evaluated to assess product reliability. Finite-element analyses (FEA) are done on the NTU CRAY T94 to calculate hygrothermally induced anisotropic viscoelastic deformations and stresses in plastic IC packages during surface-mounting processes. Numerical results show that substantially high stresses in silicon chips and lead frames occur when LOC TSOP packages are exposed to reflow soldering processes. Numerical results also demonstrate that residual stress values in IC packages are sensitive not only to the magnitude of the loads but also to the loading history because of the hygro-thermo-viscoelastic behavior of plastic mold compound IC materials.

^ Finite-Element Analysis of Thick Thermosetting Matrix Composite Manufacturing Cure Process
S. Yi* (Nanyang), H. H. Hilton*
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

A transient heat transfer finite-element model is introduced to simulate the curing process of polymer matrix composites, and a 3-D anisotropic cure simulation for a thick laminated composite is performed. The temperatures inside of the laminates can be evaluated by solving the 3-D nonlinear anisotropic heat conduction equations including the internal heat produced by chemical reactions. The internal heat generation term can be expressed in terms of the cure rate. Correlation between experimentally measured and predicted temperature gradients is presented for various cure cycle histories. Probabilities of delamination during cure are evaluated.

^ Free Edge Stresses in Elastic and Viscoelastic Composite Laminates under Uniaxial Extension, Bending, and Twisting Loadings
S. Yi* (Nanyang), H. H. Hilton*
University of Illinois; Nanyang Technological University; National Center for Supercomputing Applications; U.S. Department of Energy, DAHC94-96-C-0005 (HPCMP-PET)

Interlaminar stresses near free laminate edges may result in delamination onset and growth and also may result from mismatches in layer properties. Little is known about interlaminar stresses caused by bending and/or twisting loads. A finite-element procedure for the analysis of time-dependent interlaminar stresses in elastic and viscoelastic laminated composites subjected to arbitrary combinations of axial extension, bending, and/or twisting loads is developed based on displacement fields for laminates under a generalized plane deformation state. Parametric studies are presented to demonstrate the accuracy of the numerical procedures.

^ Performance Evaluations of Viscoelastic Finite-Element Analyses on Coarse Grained and Massively Parallel Supercomputers
S. Yi* (Nanyang), H. H. Hilton*
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University

Performance evaluations of dynamic viscoelastic finite-element procedures and codes on coarse grained and massively parallel supercomputers such as the CRAY Y-MP, CRAY C-90, and the Connection Machine 5 (CM-5) have been undertaken. The element stiffness computations are in the range of 73 to 183 mega floating-point operations per second (Mflops) on the NCSA CRAY Y-MP. Using four node plane elements and the 256-processor CM-5, a speedup factor of about 22 over the CRAY Y-MP was obtained for calculating 1.6x105 element stiffness matrices, which is 1.65 Gflops. The performances of the conjugate gradient method on the CRAY Y-MP and CM-5 are also evaluated and are compared with those of the Cray sparse matrix and of the Feable solvers.

^ Process-induced Residual Thermal Stresses and Deformations in Thick Thermosetting Matrix Composite Laminates
S. Yi* (Nanyang), H. H. Hilton*
University of Illinois; National Center for Supercomputing Applications; Nanyang Technological University; U.S. Department of Energy, DAHC94-46-C-0005 (HPCMP-PET)

A transient heat transfer, finite-element model is introduced to simulate the curing process of polymer matrix composites. Temperature distributions inside the laminates are evaluated by solving the nonlinear anisotropic heat conduction equations, which include the internal heat produced by chemical reactions. The internal heat generation contribution is expressed in terms of cure rates. Correlations between experimentally measured and predicted temperature gradients are found for various cure cycle histories. The effects of temperature and cure rate on viscoelastic responses of graphite-epoxy laminated composites are investigated using finite-element analyses. Residual stresses for these composite plates subjected to temperature cycles are also determined.


Summary of Engineering Research