The parameterized level set method for structural topology optimization with shape sensitivity constraint factor

Cui, Mingtao; Luo, Chenchun; Li, Guang; Pan, Min

doi:10.1007/s00366-019-00860-8

Cited by 26 publications

(3 citation statements)

References 47 publications

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“…Ever since the homogenization method for TO was proposed in 1988 [2], research on the TO of continuum structures has expanded rapidly. Numerous methods and approaches have been discussed and developed, including homogenization [2][3][4][5][6], evolutionary structural optimization (ESO) [7][8][9], bidirectional evolutionary structural optimization (BESO) [10][11][12], phase-field [13][14][15][16][17], level-set [18][19][20][21][22][23][24], the method of moving morphable components [25,26], and the solid isotropic material with penalization (SIMP) approach [27][28][29][30].…”

Section: Introduction 1topology Optimization (To)mentioning

confidence: 99%

Bisection Constraint Method for Multiple-Loading Conditions in Structural Topology Optimization

Pham-Truong,

Kawamura,

Okada

2023

Applied Sciences

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Topology optimization (TO) is currently a focal point for researchers in the field of structural optimization, with most studies concentrating on single-loading conditions. However, real engineering structures often have to work under various loading conditions. Approaches addressing multiple-loading conditions often necessitate subjective input in order to determine the importance of each loading condition, aiming for a compromise between them. This paper proposes a so-called bisection constraint method (BCM), offering a unique, user-preference-independent solution for TO problems amidst multiple-loading conditions. It is well-known that minimizing the system’s compliance is commonly used in TO as the objective. Generally, compliance is not as sufficient as stress to be used as a response to evaluate the performance of structures. However, formulations focusing on minimizing stress levels usually pose significant difficulties and instabilities. On the other hand, the compliance approach is generally simpler and more capable of providing relatively sturdy designs. Hence, the formulation of min–max compliance is used as the target problem formulation of the proposed method. This method attempts to minimize compliance under only one loading condition while compliances under the remaining loading conditions are constrained. During the optimization process, the optimization problem is automatically reformulated with a new objective function and a new set of constraint functions. The role of compliance under different loading conditions, i.e., whether it is to be treated as an objective or constraint function, might be changed throughout the optimization process until convergence. Several examples based on the solid isotropic material with penalization (SIMP) approach were conducted to illustrate the validity of the proposed method. Furthermore, the general effectiveness of the compliance approach in terms of stress levels is also discussed. The calculation results demonstrated that while the compliance approach is effective in several cases, it proves ineffective in certain scenarios.

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Section: Introduction 1topology Optimization (To)mentioning

confidence: 99%

Bisection Constraint Method for Multiple-Loading Conditions in Structural Topology Optimization

Pham-Truong,

Kawamura,

Okada

2023

Applied Sciences

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“…Actually, stiffener layout optimization is the problem for searching optimal material distribution [5], and topology optimization has become the most popular tool for stiffener layout design [6]. The advantage of structure topology optimization is using the same material to obtain better mechanics and thermotics performance [7].…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization of Stiffener Layout Design for Box Type Load-Bearing Component under Thermo-Mechanical Coupling

Yang¹,

Xiong²,

Du³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The structure optimization design under thermo-mechanical coupling is a difficult problem in the topology optimization field. An adaptive growth algorithm has become a more effective approach for structural topology optimization. This paper proposed a topology optimization method by an adaptive growth algorithm for the stiffener layout design of box type load-bearing components under thermo-mechanical coupling. Based on the stiffness diffusion theory, both the load stiffness matrix and the heat conduction stiffness matrix of the stiffener are spread at the same time to make sure the stiffener grows freely and obtain an optimal stiffener layout design. Meanwhile, the objectives of optimization are the minimization of strain energy and thermal compliance of the whole structure, and thermo-mechanical coupling is considered. Numerical studies for square shells clearly show the effectiveness of the proposed method for stiffener layout optimization under thermo-mechanical coupling. Finally, the method is applied to optimize the stiffener layout of box type load-bearing component of the machining center. The optimization results show that both the structural deformation and temperature of the load-bearing component with the growth stiffener layout, which are optimized by the adaptive growth algorithm, are less than the stiffener layout of shape '#' stiffener layout. It provides a new solution approach for stiffener layout optimization design of box type load-bearing components under thermo-mechanical coupling.

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“…Islam et al 32 and Wei et al 33 studied the basis functions in the parameterized level set method. Cui et al 34 controlled the step size in the iterative process by increasing the shape sensitivity constraint factor in the parameterized level set method. Wei et al 35 proposed a multi‐discretization method based on the parameterized level set method, in which coarse discretization was used to analyze structure and dense discretization to express structural topology.…”

Section: Introductionmentioning

confidence: 99%

Concurrent topology optimization of multiple components sharing partial design domain based on distance regularized parameterized level set method

Sheng

Xie

2023

Numerical Meth Engineering

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In this article, the distance regularized parameterized level set method (DRPLSM) is proposed, which introduces a specified energy functional into the level set equation as the distance regularization term. Geometric verification shows that the distance regularization scheme keeps the level set function near the structural boundary as an approximate signed distance function. Based on benchmark example of the cantilever beam, it is verified that the DRPLSM can avoid the re‐initialization of level set function in the optimization process and obtain smooth structural boundary. The DRPLSM is applied to multicomponent concurrent topology optimization with partially shared design domain for the first time. It makes the optimization results have smooth structural boundaries. The optimization objective of this algorithm is to minimize the structural compliance of all components. The sharing domain is divided into different design domains according to the strain energy of elements. The optimality of the proposed algorithm for partitioning the sharing domain is verified using the literature example with known optimal solutions. A symmetric structure example, a main and auxiliary optimization structure example and an example with design‐dependent boundary loads show that the proposed concurrent optimization algorithm has wide applicability.

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The parameterized level set method for structural topology optimization with shape sensitivity constraint factor

Cited by 26 publications

References 47 publications

Bisection Constraint Method for Multiple-Loading Conditions in Structural Topology Optimization

Bisection Constraint Method for Multiple-Loading Conditions in Structural Topology Optimization

Topology Optimization of Stiffener Layout Design for Box Type Load-Bearing Component under Thermo-Mechanical Coupling

Concurrent topology optimization of multiple components sharing partial design domain based on distance regularized parameterized level set method

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