Applications of Parallel and Vector Algorithms in Nonlinear Structural Dynamics Using the Finite Element Method

摘要

This research is directed toward the numerical analysis of large, three dimensional, nonlinear dynamicproblems in structural and solid mechanics. Such problems include those exhibiting large deformations,displacements, or rotations, those requiring finite strain plasticity material models that couple geometricand material nonlinearities, and those demanding detailed geometric modeling.A finite element code was developed, designed around the 3D isoparametric family of elements, and using aTotal Lagrangian formulation and implicit integration of the global equations of motion. The research wasconducted using the Alliant FX/8 and Convex C240 supercomputers.The research focuses on four main areas:Development of element computation algorithms that exploit the inherent opportunities for concurrencyand vectorization present in the finite element method; Comparison of the preconditioned conjugate gradientmethod to a representative direct solver; Investigation of various nonlinear solution algorithms, such asmodified Newton-Raphson, secant-Newton, and nonlinear preconditioned conjugate gradient; and,Discovery of an accurate, robust finite strain plasticity material model.