PARALLEL-VECTOR COMPUTATIONS FOR GEOMETRICALLY NONLINEAR FINITE-ELEMENT ANALYSIS

Existing procedures for nonlinear finite element analysis are reviewed. Common computational steps among existing methods are identified. Parallel-vector solution strategies for the generation and assembly of element matrices, solution of the resulting system of linear equations, calculations of the unbalanced loads, displacements and stresses are all incorporated into the Newton-Raphson (NR), modified Newton-Raphson (mNR), and BFGS methods. Furthermore, a mixed parallel-vector Choleski-Preconditioned Conjugate Gradient (C-PCG) equation solver is also developed and incorporated into the piecewise linear procedure for nonlinear finite element analysis. Numerical results have indicated that the Newton-Raphson method is the most effective nonlinear procedure and the mixed C-PCG equation solver offers substantial computational advantages in a parallel-vector computer environmnent.