Topology optimization using a topology description function

Ruiter, M.J. de; Keulen, Fred van

doi:10.1007/s00158-003-0375-7

Cited by 76 publications

(36 citation statements)

References 24 publications

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“…Several different parameterization schemes have been proposed. A popular approach is to use radial basis functions (Norato et al 2004;De Ruiter and Van Keulen 2004;Luo et al 2007;Pingen et al 2010). Other parameterization methods are the spectral level-set method (Gomes and Suleman 2006), Kriging-based (Hamza et al 2014) and an approach based on the intersection of a cutting plane and an implicit signed-distance function, recently proposed by the author (Dunning 2017).…”

Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

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This paper introduces explicit minimum length-scale constraint functions suitable for parameterized implicit function based topology optimization methods. Length-scale control in topology optimization has many potential benefits, such as removing numerical artifacts, mesh independent solutions, avoiding thin, or single node hinges in compliant mechanism design and meeting manufacturing constraints. Several methods have been developed to control length-scale when using density-based or signed-distance-based level-set methods. In this paper a method is introduced to control length-scale for parameterized implicit function based topology optimization. Explicit constraint functions to control the minimum length in the structure and void regions are proposed and implementation issues explored in detail. Several examples are presented to show the efficacy of the proposed method. The examples demonstrate that the method can simultaneously control minimum structure and void length-scale, design hinge free compliant mechanisms and control minimum length-scale for three dimensional structures.

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Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

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“…Since this pioneering work, various node-based topology optimization methods have been reported. Reiter and Keulen [23] developed a topology optimization method, where Radial Basis Functions are used to generate the TDF. Genetic algorithm is applied but with large computational costs.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Yang

Liu

Yang

et al. 2018

Mathematical Problems in Engineering

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Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

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“…As a result, the second category is the development of alternative level set methods [25][26][27][28][29][30][31] for shape and topology optimization of structures, without directly solving the H-J PDE. For instance, Belytscko et al [29] proposed a "narrow band" method, which represented the level set surface within a range of the zero level set boundaries, based on a set of nodal variables of the level set function.…”

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confidence: 99%

“…Haber [30] proposed a multilevel continuation scheme, in which SQP was applied to update the implicit shape boundary rather than directly solving the H-J PDE. De Ruiter and Kenlen [31] developed a topological description function method, which only employed the concept of the implicit level set boundary representation to geometrically describe the design boundary, without the consideration of the H-J PDE. Luo et al [20] proposed a semi-implicit level set method for structural optimization, that is, a semi-implicit additive operator splitting (AOS) scheme rather than the FDM was utilized to solve the H-J PDE numerically.…”

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confidence: 99%

A Short Survey: Topological Shape Optimization of Structures Using Level Set Methods

Luo¹

2013

J Appl Mech Eng

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Over the past two decades, a relatively new field known as topology optimization is rapidly expanding in computational design research. In contrast to the detailed designs (e.g. size and shape optimizations) of a structure, topology optimization [1] is highly challenging at the conceptual design stage, because it requires automatic determination of an optimal material layout of a structure in conjunction with an optimal shape of the boundary, to make cost-efficient use of a given amount of material for improving the concerned structural performance. Topology optimization can be regarded as an iterative numerical procedure to re-distribute the material in a fixed reference domain subject to boundary conditions. The optimal topology of the structure can be obtained, in association with an optimal material connectivity, when a pre-defined objective function reaches its extremity under specific constraints. Topology optimization has been applied to a broad range of existing research areas [1], and is continuously being introduced to many new and emerging areas, as an enabling persuasive design technique.Several typical methods have been developed for topology optimization of structures, including the homogenization method [2], the SIMP (Solid Isotropic Material with Penalization) approach [3,4] and the level set-based method [5][6][7][8]. Topology optimization essentially belongs to a family of integer programming problems with a large number of discrete design variables. On one hand, many wellestablished more efficient gradient-based optimization algorithms cannot be directly applied, due to the discrete nature of the problem. On the other hand, conventional discrete optimization algorithms, such as the genetic algorithms, may not be used to effectively find the solution of such large-scale discrete optimization problems, due to the "NP-Hard" difficulty. To this end, the homogenization and SIMP are two typical methods, which have been widely used to relax the original discrete optimization problem, to allow the discrete design variables taking intermediate values ranging from 0 to 1.In particular, SIMP, as an extension of the homogenization method, has received popularity in the area of structural optimization, due to its conceptual simplicity and implementation easiness. SIMP has already had several variant formulations, including elemental density based SIMP [4], nodal density based SMIP [9] and meshless field points based SIMP [10]. With SIMP, the original discrete optimization is changed to AbstractThis paper will give a short survey about topology optimization of structures. It is particularly focused on topological shape optimization of structures using level-set methods, including the level-set based standard methods and the level-set based alternative methods. The former often directly solve the Hamilton-Jacobi partial differential equation (H-J PDE) to obtain the boundary velocity field using Finite Differential Methods (FDM), and the later commonly employ parametric or equivalent methods to evaluate the ...

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Topology optimization using a topology description function

Cited by 76 publications

References 24 publications

Minimum length-scale constraints for parameterized implicit function based topology optimization

Minimum length-scale constraints for parameterized implicit function based topology optimization

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

A Short Survey: Topological Shape Optimization of Structures Using Level Set Methods

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