Recursive block-by-block integral equation solution for transient dynamic analysis with memory-type elements

Abstract

An efficient method of computing structural response of multi-story nonlinear base isolated buildings for a given seismic event is presented. Using a recursive block-by-block convolution (RBBIEF) solution to the governing nonlinear Volterra integral equation, structural base motion acting through an arbitrary number of nonlinear base isolators can be computed quickly and accurately. The general solution to the governing nonlinear Volterra integral is formulated and subsequently converted into code using MATLAB. The procedure incorporates modal properties, computed from conventional finite element (FE) techniques, and the generated MATLAB programs to solve a varying set of multi- degree of freedom structures coupled to both linear and nonlinear isolators. Ultimately, an analysis is conducted on a 30-story building that was overly designed using the 1994 Load Resistance Factor Design Ref. 1 and the 1994 Uniform Building Codes Ref. 2 for earthquake loading. The method demonstrates that the Volterra integration scheme in the time domain is very effective and efficient.