Incremental Solution Procedure for Nonlinear Structural Dynamics Problems

Abstract

A general incremental formulation is presented for solving nonlinear structural dynamic problems. The formulation introduces a new term which is not obtained in the usual finite element tangent stiffness approach. The generality of the derivation is used to show how the computation of the geometric stiffness matrix can be eliminated and its contribution included through a simple addition of the estimated incremental displacements to the equilibrium correction term. This approximation thus has the potential for saving significant computing time in the assemblage of higher order finite elements. Two simple numerical experiments are conducted and it is shown that accuracy is still retained when this approximation is used.