A boundary element and level set based topology optimisation using sensitivity analysis

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe structural topology optimisation method presented in this paper is based on the boundary element method, level set method and shape sensitivity analysis for two-dimensional linear elastic problems. The proposed method automatically nucleates holes within the design domain during the optimisation process using a topological derivative based hole insertion criterion. The level set method is used to provide an implicit description of the structural geometry, which is capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. During the optimisation process non-uniform rational b-splines are fitted through the zero level set contours, which links an implicit geometry representation to its structural model. In addition, this provides an optimal design in standard CAD format, and without intermediate material densities, which can be directly used in other design processes. The proposed optimisation method is tested against different benchmark examples and the optimal geometries generated are in close agreement those available in the literature of topology optimisation.

Manufacturing cost and reliability‐based shape optimization of plate structures

“…Previous work on the topic of shape optimization with the BEM by the research community has mostly considered 2D structures, [1][2][3][4][5][6][7][8][9][10][11] and to a lesser-degree 3D structures. [12][13][14][15][16][17][18] Very few previous works by the research community on the topic of shape optimization with the BEM have considered plate or shell structures.…”

Explicit structural topology optimization using boundary element method‐based moving morphable void approach

“…It is also worth noting that BEM has successfully incorporated into topology optimization. [47][48][49] However, to combine BEM with topology optimization, exact structural boundary must be firstly provided for mesh construction. Due to the implicit geometry representation, this requirement is not easy to implement in traditional topology optimization approaches.…”

“…Generally, since BEM works by constructing a mesh over the modeled boundary (in 2D), it has great potential to solve the aforementioned issues. It is also worth noting that BEM has successfully incorporated into topology optimization 47–49 . However, to combine BEM with topology optimization, exact structural boundary must be firstly provided for mesh construction.…”

“…In Reference 48, internal points are predistributed for hole detection over the whole design domain, and a weighted Delaunay triangularization algorithm is then adopted for remeshing. In Reference 49, NURBS‐based geometry is reconstructed through the level set function for BE mesh generation purpose. In the present article, a topology optimization approach under the MMV solution framework incorporating BEM is proposed.…”

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

“…• the boundary element method (BEM) based boundary only discretisation The reduction of problem dimensionality with the use of BEM based body conforming mapping is very attractive as compared to the FEM based domain discretisation. In the literature of structural optimisation, researchers combined the BEM with the LSM for the solution of optimisation problems in both two and three-dimensions, e.g, compliance minimisation [10,11,12,13], sound scattering [14,15], heat conduction [16], etc.…”