Boundary Elements in Shape Optimal Design of Structures

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.

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“…According to Soares and Choi [29], for a linear material the first variation of the objective function, (i.e. Equation (2)) becomes…”

Section: Shape Sensitivity Analysismentioning

confidence: 99%

“…Soares and Choi [29] used the Pshenichny linearisation method [30] of linear programming in combination with the boundary element method to solve the optimisation problem. However, the optimisation problem can also be solved with the Lagrange multiplier method as:…”

Section: Shape Sensitivity Analysismentioning

confidence: 99%

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

Ullah

Trevelyan

2016

Engineering Analysis with Boundary Elements

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“…The term −k(∇T · ∇ ) in (27) can be expressed as −k(∇ n · ∇ n + ∇ ⊥ T · ∇ ⊥ ). Likewise the term ∇ n ( q) generates the expression k(∇ n T · ∇ n ), which therefore cancels in (27) It can be shown [15] that = div n, which can be approximated by div Á. Consider the triangular element depicted in Figure A2.…”

Section: Appendix Amentioning

confidence: 97%

“…Haug et al [14] used the method of Reference [13] to formulate sensitivity expressions for structural problems and used the FEM to solve the state and adjoint equations. Soares and Choi [15] used the method of Reference [14] to form an adjoint structure for a stress constraint and suggested using the BEM to solve the state and adjoint equations. Park and Yoo [16] showed that for problems governed by the Laplace operator, a unique solution of the boundary integral equation exists and is identical to the variational solution in the Sobolev space H 1 ( ) [17].…”

Section: Introductionmentioning

confidence: 99%

Novel cooling channel shapes in pressure die casting

Clark

Davey

Hinduja

2001

Numerical Meth Engineering

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SUMMARYThe pressure die casting involves die designs incorporating cooling channels positioned to facilitate the controlled extraction of energy from a solidifying casting. It is now known that subcooled nucleate boiling can occur in cooling channels and this paper is concerned with novel cooling channel shapes that are optimized to promote and enhance this boiling and thus reduce casting times. Shape sensitivity analysis is applied to a boundary element model using the material derivative adjoint variable technique. Mesh node positions on the cooling channels are used as the design parameters. The sensitivities are used in a conjugate gradient non-linear optimization routine. It is shown that with this approach cooling channels can be designed to maximize boiling heat transfer whilst at the same time allow some degree of control of spatial temperature variation over the die cavity surface. Simulation and experimental results are presented for a traditional die and an optimized die. A 60 per cent reduction in cycle time is achieved with the optimized die.

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“…Defourny 1986). A survey of such efforts was given by Mota Soares and Choi (1986), Earle and Saigal (1988) and Bedair (1991). In the area of the sensitivity analysis of elastic continua, efforts to date have been directed towards the Direct Boundary Element Method (DBEM).…”

Section: Introductionmentioning

confidence: 99%

Shape sensitivity analysis using the indirect boundary element method

Bedair

Thompson

1993

Structural Optimization

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A b s t r a c tThe paper describes a novel formulation for the computation of the design sensitivities required for shape optimization problems using the indirect boundary element method. As a first stage, the system of equations that evaluate the fictitious traction sensitivities is differentiated with respect to shape design variables. The stress or displacement sensitivities are then evaluated by direct substitution of the fictitious traction sensitivities into the differentiated stress or displacement kernels. Two other finite difference-based techniques for the evaluation of the stress sensitivities, using the indirect boundary element method are also presented. The advantages and the drawbacks of each approach are discussed. These methods have been shown to be effective, accurate and can be incorporated in an existing BE code with much less programming effort than other BE-based techniques. The efficiency of the three methods is illustrated by optimizing the shape of a 900 V-n0tch. In all cases, convergence is achieved within three to four iterations.Various approximate techniques are suggested to minimize the computation cost of the optimization problem. These techniques are based on the fundamental features of the stress field, the differentiated kernels and the system of matrices of the optimization problem. Investigations have shown that employing these techniques yields more than a 50% reduction in computer time with insignificant loss of accuracy. I n t r o d u c t i o nResearch into shape optimization has been largely motivated with the increasing demands for achieving more costcompetitive designs. Since this class of optimization problems is non-linear in nature, an iterative procedure is normally necessary to achieve an optimum design. Most of the work on numerical shape optimization is based on finite element formulations (e.g. Francavilla et al.

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Boundary Elements in Shape Optimal Design of Structures

Cited by 33 publications

References 15 publications

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

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

Novel cooling channel shapes in pressure die casting

Shape sensitivity analysis using the indirect boundary element method

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