A boundary element and level set based bi-directional evolutionary structural optimisation with a volume constraint

Ullah, B.; Trevelyan, J.; Islam, S.

Abstract

A new topology optimisation algorithm is implemented and presented for compliance minimisation of continuum structures using a volume preserving mechanism which effectively handles a volume constraint. The volume preserving mechanism is based on a unique combination of the level set method and a boundary element based bi-directional evolutionary structural optimisation approach using a bisectioning algorithm. The evolving structural geometry is implicitly represented with the level sets, efficiently handling complex topological shape changes, including holes merging with each other and with the boundary. Numerical results for two-dimensional linear elasticity problems suggest that the proposed adaptation provides smooth convergence of the objective function and a more robust, smoother geometrical description of the optimal design. Moreover, this new implementation allows for efficient material re-distribution within the design domain such that the objective function is minimised at constant volume. The proposed volume preserving mechanism can be easily extended to three-dimensional space.

Citation

Ullah, B., Trevelyan, J., & Islam, S. (2017). A boundary element and level set based bi-directional evolutionary structural optimisation with a volume constraint. Engineering Analysis with Boundary Elements, 80, 152-161. https://doi.org/10.1016/j.enganabound.2017.02.012

• Journal Article Type: Article
• Acceptance Date: Feb 10, 2017
• Online Publication Date: May 5, 2017
• Publication Date: Jul 1, 2017
• Deposit Date: Feb 16, 2017
• Publicly Available Date: May 5, 2018
• Journal: Engineering Analysis with Boundary Elements
• Print ISSN: 0955-7997
• Electronic ISSN: 1873-197X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 80
• Pages: 152-161
• DOI: https://doi.org/10.1016/j.enganabound.2017.02.012
• Public URL: https://durham-repository.worktribe.com/output/1365382