Boundary‐Element Direct Reanalysis for Continuum Structures

Abstract

Concepts involving direct approaches for continuum structural reanalysis of modified shapes employing the boundary‐element analysis (BEA) method are considered. A boundary‐element zone‐condensation technique is shown to form a very general and competitive approach for reanalysis of BEA models. Zone condensation involves the employment of multizone BEA models where the degrees of freedom and corresponding matrix coefficients in each zone are collected in partitions (also called blocks). These partitioned‐zone matrix equations can be strategically manipulated to eliminate (or condense) unchanging blocks from the overall BEA system equations, thus allowing for the subsequent assembly into an overall set of matrix equations of smaller size than when zone condensation is not employed. This approach to direct reanalysis is contrasted with strategies that utilize the well‐known Sherman‐Morrison‐Woodbury identity for the inverse of a modified matrix. Test cases are discussed to demonstrate the effectiveness of the strategies presented. Timing, storage, and accuracy results are included in these studies.