| This research is directed toward the analysis of large, three dimensional, nonlinear dynamic problems in structural and solid mechanics. Such problems include those exhibiting large deformation, displacements, or rotations, those requiring finite strain plasticity material models that couple geometric and material nonlinearities, and those demanding detailed geometric modeling. The finite element method based on a Total Lagrangian approach and performing an implicit solution of the global equations of motion is employed to model these problems. The resulting computer program was designed around the use of the 3D isoparametric family of elements. The research was conducted using the Alliant FX/8 and Convex C240 supercomputers. The research focuses on four main areas: (1) The development of element computation algorithms so that the inherent opportunities for concurrency and vectorization present in the finite element method can be exploited. Optimizing compilers are not sufficient for dealing with complications such as data dependencies and are not equipped to recognize opportunities to restructure code to achieve a higher level of concurrency and a consistently efficient vector length. Because of this, compiler optimized finite element code written for sequential computers can be inefficient when executed on supercomputers. (2) The comparison of the preconditioned conjugate gradient method to a representative direct solver. The solution of a linear system of equations is generally required for each equilibrium iteration in a nonlinear analysis. Traditionally, a direct solver has been used to perform this linear solution. However, given the memory requirements and computational effort characteristic of a direct solver, iterative methods are more appropriate for large problems solved on supercomputers. The element-by-element (EBE) and diagonal preconditioners are employed. (3) The investigation of various nonlinear solution algorithms, such as modified Newton-Raphson, secant-Newton, and nonlinear preconditioned conjugate gradients. (4) The discovery of an accurate and robust finite strain plasticity material model so that material nonlinearities can be evaluated both in the presence and the absence of geometric nonlinearities. The primary focus is on the formulation of the constitutive equations governing {dollar}Jsb2{dollar} flow theory using strains-stresses and their rates defined on the unrotated frame of reference. |
