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research-article

A Taylor expansion approach for computing structural performance variation from population-based shape data

[+] Author and Article Information
Xilu Wang

Computational Design & Manufacturing Laboratory, Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53705
xwang666@wisc.edu

Xiaoping Qian

Computational Design & Manufacturing Laboratory, Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53705
qian@engr.wisc.edu

1Corresponding author.

ASME doi:10.1115/1.4037252 History: Received February 15, 2017; Revised May 25, 2017

Abstract

Rapid advancement of sensor technologies and computing power has led to wide availability of massive population-based shape data. In this paper, we present a Taylor expansion based method for computing structural performance variation over its shape population. The proposed method takes four steps: 1) learning the shape parameters and their probabilistic distributions through the statistical shape modeling; 2) deriving analytical sensitivity of structural performance over shape parameter; 3) approximating the explicit function relationship between the FE solution and the shape parameters through Taylor expansion; 4) computing the performance variation by the explicit function relationship.

To overcome the potential inaccuracy of Taylor expansion for highly nonlinear problems, a multi-point Taylor expansion technique is proposed, where the parameter space is partitioned into different regions and multiple Taylor expansions are locally conducted. It works especially well when combined with the dimensional reduction of the principal component analysis in the statistical shape modeling.

Numerical studies illustrates the accuracy and efficiency of this method.

Copyright (c) 2017 by ASME
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