Research Papers

A Parallel Reanalysis Method Based on Approximate Inverse Matrix for Complex Engineering Problems

[+] Author and Article Information
Hu Wang, Guangyao Li

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China

Enying Li

Collage of Transportation and Logistics,
Central South University of Forestry and Technology,
Changsha, Hunan 410004, China

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 17, 2011; final manuscript received April 4, 2013; published online May 30, 2013. Assoc. Editor: Olivier de Weck.

J. Mech. Des 135(8), 081001 (May 30, 2013) (8 pages) Paper No: MD-11-1432; doi: 10.1115/1.4024368 History: Received October 17, 2011; Revised April 04, 2013

The combined approximations (CA) method is an effective reanalysis approach providing high quality results. The CA method is suitable for a wide range of structural optimization problems including linear reanalysis, nonlinear reanalysis and eigenvalue reanalysis. However, with increasing complexity and scale of engineering problems, the efficiency of the CA method might not be guaranteed. A major bottleneck of the CA is how to obtain reduced basis vectors efficiently. Therefore, a modified CA method, based on approximation of the inverse matrix, is suggested. Based on the symmetric successive over-relaxation (SSOR) and compressed sparse row (CSR), the efficiency of CA method is shown to be much improved and corresponding storage space markedly reduced. In order to further improve the efficiency, the suggested strategy is implemented on a graphic processing unit (GPU) platform. To verify the performance of the suggested method, several case studies are undertaken. Compared with the popular serial CA method, the results demonstrate that the suggested GPU-based CA method is an order of magnitude faster for the same level of accuracy.

Copyright © 2013 by ASME
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Fig. 2

Block and thread of CUDA

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Fig. 3

Flowchart of the parallel CA on CUDA platform

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Fig. 1

Arrays A, JA, and IA comprise the CSR representation of original one

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Fig. 4

An illustration of communication graph for a simple mesh

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Fig. 5

An illustration of colored elements

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Fig. 9

The initial simple CAD model (unit mm) of example III

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Fig. 7

CAD model of a door inner and corresponding load

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Fig. 8

Mesh models of the initial and changed structure of example II

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Fig. 10

Sizes of the cross-section of vertical beam (unit mm) of example III

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Fig. 11

Initial FE model and constraints enforcement nodes example III

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Fig. 12

Initial solution by the complete analysis of example III

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Fig. 13

The modified simple CAD model (unit mm) of example III

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Fig. 14

Approximation response by the parallel CA method of example III

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Fig. 15

Response of modified structure by the complete method of example III




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