Development of a genetic algorithm-based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problems

Abstract

It is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres, Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper, we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy. Example problems are solved which demonstrate the effectiveness of the procedure. Copyright © 2006 John Wiley & Sons, Ltd.