Material cloud method for topology optimization

Chang, Sung‐Pil; Youn, Sung‐Kie

doi:10.1002/nme.1508

Cited by 12 publications

(6 citation statements)

References 39 publications

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“…In general, they use a fixed FE grid for numerical analysis, thus design results are highly dependent on the initial fixed computational mesh. Although the studies on design space expansion were presented in 2D problems (Chang and Youn, 2006;Jang and Kwak, 2008), the initial grid dependency problem is very difficult to resolve in optimization of shell problems. Moreover, the topology optimization methods which use cell-based representation such as SIMP, ESC, ECP and MC, etc.…”

Section: Introductionmentioning

confidence: 99%

“…The ECP can provide excellent designs in geometrically nonlinear problems since unrealistic effect on distortion of low density elements is eliminated. The material cloud (MC) method was proposed by Chang and Youn (2006). The optimal topology is expressed by means of the material clouds and the size and/or position of them are design variables in the material cloud method based topology optimization.…”

Section: Introductionmentioning

confidence: 99%

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Shape optimization and its extension to topological design based on isogeometric analysis

Seo

Kim

Youn

2010

International Journal of Solids and Structures

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121

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a b s t r a c tIn most of structural optimization approaches, finite element method (FEM) has been employed for structural response analysis and sensitivity calculation. However, the approaches generally suffer certain drawbacks. In shape optimization, cumbersome parameterization of design domain is required and time consuming remeshing task is also necessary. In topology optimization, design results are generally restricted on the initial design space and additional post-processing is required for communication with CAD systems. These drawbacks are due to the use of different mathematical languages in design or geometric modeling and numerical analysis: spline basis functions are used in design and geometric modeling whereas Lagrangian and Hermitian polynomials in analysis. Isogeometric analysis is a very attractive and promising alternative to overcome the limitations resulting from the use of the conventional FEM in structural optimization. In isogeometric analysis, the same spline information such as control points and spline basis functions which represent geometries in CAD systems are also used in numerical analysis. Such unification of the mathematical languages in CAD, analysis and design optimization can resolve the issues mentioned above. In this work, structural shape optimization using isogeometric analysis is studied on 2D and shell problems. The proposed framework is extended to topology optimization using trimming techniques. New inner fronts are introduced by trimming spline curves in topology optimization. Trimmed surface analysis which was recently proposed to analyze arbitrary complex topology problems is employed for topology optimization. Some benchmarking problems in shape and topology optimization are treated using the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shape optimization and its extension to topological design based on isogeometric analysis

Seo

Kim

Youn

2010

International Journal of Solids and Structures

Self Cite

121

View full text Add to dashboard Cite

show abstract

“…One can observe over the last two decades the implementation of various specific methods ranging from gradient-based approaches, e.g., Reference [6], where mathematical models are derived to calculate the sensitivities of design variables to non-gradient-based ones, where the material is redistributed using various, usually heuristic techniques. In what follows, the generation of optimal topologies involves, among others, evolutionary ESO/BESO structural optimization [11,12], genetic algorithms [13,14], other biologically inspired algorithms [15,16], the material cloud method [17], spline based topology optimization [18], level set method [19,20], cellular automata [21,22,23,24,25,26] or the moving morphable components approach [27,28]. It can be seen from the above that traditional gradient-based mathematical programming algorithms are more readily replaced by novel and efficient heuristic methods inspired by biological, chemical or physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

GHOST—Gate to Hybrid Optimization of Structural Topologies

Bochenek

Tajs-Zielińska

2019

Materials

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Although well-recognized in the fields of structural and material design and widely present in engineering literature, topology optimization still arouses a high interest within research communities. Moreover, it is observed that the development of innovative, efficient and versatile methods is one of the most important issues stimulating progress within the topology optimization area. Following this activity, in the present study, a concept of a hybrid algorithm developed in order to generate optimal structural topologies of minimal compliance is presented. The hybrid algorithm is built based on two existing approaches. The first one makes use of the formal optimality criterion, whereas the second one utilizes a special heuristic rule of design variables updating. The main idea that stands behind the concept of the present proposal is to take the advantage of both algorithms capabilities. In a numerical implementation of the hybrid algorithm, the design variables are updated at each iteration step using both approaches, and the solution with a lower objective function value is selected for the next iteration. The numerical tests of the generation of minimal compliance structures have been performed for chosen structures including a real engineering one. It has been confirmed that the proposed hybrid technique based on switching between the considered rules allows the final structures having lower values of compliance as compared with the results of an application of basic algorithms running separately to be obtained. Moreover, based on promising results of the tests performed, one can consider the proposed concept of a hybrid algorithm as an alternative for other existing topology generators.

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“…Kaveh et al, 2008), material cloud method (e.g. Chang and Youn, 2006), spline-based topology optimization (e.g. Eschenauer et al, 1993) and level set method (e.g.…”

Section: Introductory Remarksmentioning

confidence: 99%

GOTICA - generation of optimal topologies by irregular cellular automata

Bochenek

Tajs-Zielińska

2016

Struct Multidisc Optim

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In recent years the Cellular Automata (CA) concept has been successfully applied to structural topology optimization problems. In the engineering implementation of CA, the design domain is decomposed into a lattice of cells, and a particular cell together with the cells to which it is connected forms a neighborhood. It is assumed that the interaction between cells takes place only within the neighborhood and the states of cells are updated synchronously in subsequent time steps according to some local rules.The majority of results that have been obtained so far were based on regular lattices of cells. However, a practical engineering analysis and design in many cases require using highly irregular meshes for complicated geometries and/or stress concentration regions. The aim of the present paper is to extend the concept of CA towards the implementation of unstructured grid of cells related to non-regular mesh of finite elements. Introducing an irregular lattice of cells allows to reduce the number of design variables without loosing the accuracy of results and without an excessive increase of the number of elements caused by using a fine mesh for a whole structure. The implementation of non-uniform cells of Cellular Automaton requires a reformulation of standard local rules, for which the influence of

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Material cloud method for topology optimization

Cited by 12 publications

References 39 publications

Shape optimization and its extension to topological design based on isogeometric analysis

Shape optimization and its extension to topological design based on isogeometric analysis

GHOST—Gate to Hybrid Optimization of Structural Topologies

GOTICA - generation of optimal topologies by irregular cellular automata

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