Large-scale topology optimization in 3D using parallel computing

Borrvall, Thomas; Petersson, Joakim

doi:10.1016/s0045-7825(01)00216-x

Cited by 182 publications

(104 citation statements)

References 18 publications

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“…However, the compliance increase is 37% when going from 225 to 27 design variables. It is also observed that the optimized designs for the three solutions using the most design variables are similar to the solution obtained using an element density-based method [30]. However, the solution using just 27 variables does not have the central lower plate that is important for increasing the stiffness of the stool.…”

Section: D Examplesupporting

confidence: 51%

“…All other numerical implementation details and parameters remain the same. The new method in 3D is demonstrated using an example from [30], shown in Figure 15. The grey zones show areas fixed in the vertical direction and, due to symmetry, only one quarter of the design domain is modeled using 24 × 24 × 48 eight-node trilinear elements for the analysis mesh.…”

Section: D Examplementioning

confidence: 99%

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Design parameterization for topology optimization by intersection of an implicit function

Dunning

2017

Computer Methods in Applied Mechanics and Engineering

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This paper introduces a new approach to topology optimization where the structural boundary is defined by the intersection of an implicit signed-distance function and a cutting surface. The cutting surface is discretized using finite element shape-function polynomials and the nodal values become the design variables during optimization. Thus, the design parameterization is separated from the analysis discretization, which enables a reduction in the number of design variables, compared with methods that use element-wise variables. The proposed method can obtain solutions with smooth boundaries and the parameterization allows solution by standard optimization methods. Several 2D and 3D examples are used to demonstrate the effectiveness of the method, including minimization of compliance and complaint mechanism problems. The results show that the method can obtain good solutions to well-known problems with smooth, clearly defined boundaries and that this can be achieved using significantly fewer design variables compared with element-based methods.

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Section: D Examplesupporting

confidence: 51%

Section: D Examplementioning

confidence: 99%

Design parameterization for topology optimization by intersection of an implicit function

Dunning

2017

Computer Methods in Applied Mechanics and Engineering

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“…Several variants of, and extensions to, the original MMA algorithm have been developed during the last decades, e.g. see Borrval and Petersson (2001), Bruyneel et al (2002) and Zillober (2002). Various approaches for enforcing global convergence have also been proposed.…”

Section: Sequential Convex Programming Algorithmsmentioning

confidence: 99%

“…These algorithms-and some related variants, e.g. see Borrval and Petersson (2001), Bruyneel et al (2002) and Zillober et al (2004)-are also known as sequential convex programming (SCP) methods (Fleury 1993;Zillober et al 2004;Duysinx et al 2009). …”

Section: Introductionmentioning

confidence: 99%

First-order sequential convex programming using approximate diagonal QP subproblems

Etman

Groenwold

Rooda

2011

Struct Multidisc Optim

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Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal-like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are wellknown examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange-Newton QP subproblems. This results in a diagonal trust-region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi-Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.

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“…Examples of established algorithms within this class include CONLIN by Fleury and Braibant (1986) and the method of moving asymptotes (MMA) by Svanberg (1987). Algorithmic variants of MMA were presented by, for example, Borrvall and Petersson (2001), Bruyneel et al (2002), and Zillober et al (2004). Groenwold and Etman (2008b) presented tailorable convex separable SAO algorithms, in which convexity and separability of the approximations was used for the efficient solution of the approximate optimization subproblems.…”

Section: Introductionmentioning

confidence: 99%

On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

Groenwold

Etman

2010

Struct Multidisc Optim

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We reflect on the convergence and termination of optimization algorithms based on convex and separable approximations using two recently proposed strategies, namely a trust region with filtered acceptance of the iterates, and conservatism. We then propose a new strategy for convergence and termination, denoted f iltered conservatism, in which the acceptance or rejection of an iterate is determined using the nonlinear acceptance filter. However, if an iterate is rejected, we increase the conservatism of every unconservative approximation, rather than reducing the trust region. Filtered conservatism aims to combine the salient features of trust region strategies with nonlinear acceptance filters on the one hand, and conservatism on the other. In filtered conservatism, the nonlinear acceptance filter is used to decide if an iterate is accepted or rejected. This allows for the acceptance of infeasible iterates, which would not be accepted in a method based on conservatism. If however an iterate is rejected, the trust region need not be decreased; it may be kept constant. Convergence is than effected by increasing the conservatism of only the unconservative approximations in the (large, constant) trust region, until the iterate becomes acceptable to the filter. Numerical results corroborate the accuracy and robustness of the method.Based on the paper entitled 'Globally convergent SAO algorithms for large scale simulation-based optimization', presented at the 8th World

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Large-scale topology optimization in 3D using parallel computing

Cited by 182 publications

References 18 publications

Design parameterization for topology optimization by intersection of an implicit function

Design parameterization for topology optimization by intersection of an implicit function

First-order sequential convex programming using approximate diagonal QP subproblems

On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations

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