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Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolver

Dunning, Peter D., Ovtchinnikov, Evgueni, Scott, Jennifer and Kim, H. Alicia 2016. Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolver. International Journal for Numerical Methods in Engineering 107 (12) , pp. 1029-1053. 10.1002/nme.5203

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Abstract

Linear buckling c onstraints are important in structural topology optimization for obtaining designs that can support the required loads without failure. During the optimization process, the critical buckling eigenmode can change; this poses a challenge to gradient-based optimization and can require the computation of a large number of linear buckling eigenmodes. This is potentially both computationally difficult to achieve and pro- hibitively expensive. In this paper, we motivate the need for a large number of linear buckling modes and show how several features of the block Jacobi conjugate gradient (BJCG) eigenvalue method, including opti- mal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts, can be used to efficiently and robustly compute a large number of buckling eigenmodes. This paper also introduces linear buckling constraints for level-set topology optimization. In our approach, the velocity function is defined as a weighted sum of the shape sensitivities for the objective and constraint functions. The weights are found by solving an optimization sub-problem to reduce the mass while maintaining feasibility of the buckling constraints. The effectiveness of this approach in combination with the BJCG method is demonstrated using a 3D optimization problem

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Engineering
Publisher: Wiley
ISSN: 0029-5981
Date of First Compliant Deposit: 29 November 2018
Date of Acceptance: 9 January 2016
Last Modified: 30 Nov 2018 15:15
URI: http://orca.cf.ac.uk/id/eprint/117202

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