Parallel-Vector Computation for Geometrically Nonlinear Frame Structural Analysis and Design Sensitivity Analysis

Parallel-vector algorithms are presented for solving the geometrically nonlinear structural problems and obtaining design sensitivity information. A new algorithm is also presented for parallel generation and assembly of the finite element stiffness and mass matrices. The presented assembly algorithm is based on a node-by-node approach rather than the more conventional element-by-element approach. Three different methods, Newton Raphson, Modified Newton Raphson, and the BFGS, are used in the analysis of the nonlinear structural problems. A study is made to determine the performance of each of the mentioned methods in a parallel-vector computer environment. Medium to large-scale, practical problems are solved to evaluate the performance of each method. A hybrid method combining the direct and iterative solvers for linear system of equations is also presented to solve the nonlinear finite element problems. The proposed hybrid method combines the use of the Choleski method and the use of the pre-conditioned conjugate gradient method, to solve the nonlinear structural problem using the piecewise linear approximation method. A different approach for achieving a parallel-vector speed for the Successive Over Relaxation method is also presented in this work. The new approach for the S.O.R method reduces the cost of communications between processors on shared memory computers. Multi-processor Cray Y-MP and Cray 2 supercomputers are used in this work