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

This research is directed toward the numerical analysis of large, three dimensional, nonlinear dynamic problems in structural and solid mechanics. Such problems include those exhibiting large deformations, displacements, or rotations, those requiring finite strain plasticity material models that couple geometric and material nonlinearities, and those demanding detailed geometric modeling. A finite element code was developed, designed around the 3D isoparametric family of elements, and using a Total Lagrangian formulation and implicit integration of the global equations of motion. The research was conducted 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 concurrency and vectorization present in the finite element method; Comparison of the preconditioned conjugate gradient method to a representative direct solver; Investigation of various nonlinear solution algorithms, such as modified Newton-Raphson, secant-Newton, and nonlinear preconditioned conjugate gradient; and, Discovery of an accurate, robust finite strain plasticity material model.Center for Supercomputing Research and Developmen