Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolverDunning, P. D., Ovtchinnikov, E., Scott, J. ORCID: https://orcid.org/0000-0003-2130-1091 and Kim, H. A. (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. ISSN 0029-5981 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1002/nme.5203 Abstract/SummaryLinear buckling constraints 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 prohibitively 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 optimal 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. Copyright © 2016 John Wiley & Sons, Ltd.
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