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Optimization of large‐scale truss structures using sparse SAND formulations
Author(s) -
Wang Qian,
Arora Jasbir S.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1773
Subject(s) - hessian matrix , truss , sequential quadratic programming , scale (ratio) , mathematical optimization , computer science , sparse matrix , quadratic programming , benchmark (surveying) , code (set theory) , algorithm , software , sample (material) , mathematics , engineering , set (abstract data type) , programming language , chemistry , physics , structural engineering , geodesy , quantum mechanics , chromatography , gaussian , geography
Abstract Sparsity features of simultaneous analysis and design (SAND) formulations are studied and exploited for optimization of large‐scale truss structures. Three formulations are described and implemented with an existing analysis code. SAND formulations have large number of variables; however, gradients of the functions and Hessian of the Lagrangian are quite sparsely populated. Therefore, this structure of the problem is exploited and an optimization algorithm with sparse matrix capability is used to solve large‐scale problems. An existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming (SQP) algorithm to solve sample problems. The formulations and algorithms work quite well for the sample problems, and their performances are compared and discussed. For all the cases considered, the SAND formulations out perform the conventional formulation except one case. Further research is suggested to fully study and utilize sparse features of the alternative SAND formulations and to develop more efficient sparse solvers for large‐scale and more complex applications. Copyright © 2006 John Wiley & Sons, Ltd.