Open Access

ARTICLE

Genetic Approaches to Iteration-free Local Contact Search

Atsuya Oishi¹, Shinobu Yoshimura²

1 Univ. Tokushima, Tokushima, JAPAN
2 Univ. Tokyo, Tokyo, JAPAN

Computer Modeling in Engineering & Sciences 2008, 28(2), 127-146. https://doi.org/10.3970/cmes.2008.028.127

Abstract

This paper describes new methods based on genetic approaches for finding approximating expressions of local coordinates of a contact point in a local contact search process. A contact search process generally consists of the following two phases: a global search phase for finding the nearest node-segment pair and a local search phase for finding an exact local coordinate of the contact point within the segment. The local contact search can be regarded as the mapping from the coordinates of nodes to the local coordinates of contact points. In this paper, two methods are proposed to find mathematical expressions that approximate the mapping in the local contact search using either the genetic algorithm (GA) or the genetic programming (GP). For both methods, parallel processing is efficiently utilized, and it enables massive search for suitable expressions in reasonable time. The GA-based method is utilized for finding approximating polynomials for the mapping in the local contact search process, while the linear GP-based method is utilized for finding approximating rational expressions. Fundamental procedures of the proposed methods are first described in detail, and next their basic performance is thoroughly tested for sample data. Finally, the proposed method using the linear GP is successfully applied to find the approximating expressions of the local coordinate value in the local contact search process for the smoothed contact surfaces with Gregory patches, and the approximating expressions obtained by the proposed method prove to be very fast in estimating the local coordinate values of the contact point.

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Keywords

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