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Structural optimization based on preconditioned conjugate gradient analysis methods
Author(s) -
Schmit Lucien A.,
Lai YeChen
Publication year - 1994
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.1620370605
Subject(s) - conjugate gradient method , mathematical optimization , truss , finite element method , computer science , sensitivity (control systems) , computation , gradient method , iterative method , algorithm , mathematics , physics , structural engineering , electronic engineering , engineering , thermodynamics
An efficient method for structural optimization is presented. Instead of classical direct decomposition methods, Preconditioned Conjugate Gradient (PCG) methods, in conjunction with two proposed starting‐vector generation schemes, are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems. These inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization. This technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints. The effectiveness of the PCG methods of analysis in structural optimization is demonstrated. Comparison among different preconditioners is made. The effect of the proposed starting‐vector generation schemes is shown. The comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis, when using PCG methods of analysis, are assessed. The parallel computation potential of PCG methods is discussed. Because of the iterative nature of PCG analysis methods and the prospects they offer for parallel computation, it is found that PCG analysis methods show promise in the context of structural optimization.