Efficient Nonlinear Transient Dynamic Analysis for Structural Optimization Using an Exact Integral Equation Formulation

Abstract

This report serves to document progress made to date on the National Science Foundation Project #97-13481, Earthquake Hazard Mitigation Program. The focus of this phase of the project is the development of an improved solution algorithm for fast transient analysis of large, locally nonlinear structures using time domain structural synthesis. The report documents the development of several algorithms intended to improve upon the original algorithm developed by the first author. The last algorithm developed meets the stated goals of the project. This algorithm is a newly developed recursive, block by block convolution solution to the governing nonlinear integral equation. As is demonstrated with a realistically large nonlinear base excitation problem (51, 300 DOF finite element model), the new algorithm provides a 78% reduction in time required for the nonlinear transient base excitation solution, as compared with traditional direct integration. The new algorithm provides an even greater reduction in computer time for subsequent analysis. The nonlinear base isolation solutions calculated using the new algorithm take approximately 7 seconds, as compared with the direct integration solution which takes approximately 30 minutes. The rapid reanalysis capability will facilitate the development of numerical optimization for the design of nonlinear isolation. The theory of transient synthesis is documented, along with a new proof of the exponential convergence properties of an iterative solution to the governing nonlinear integral equation.