Topological derivative-based topology optimization of incompressible structures using mixed formulations

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.FindingsThe description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

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Improvement of a topological level-set approach to find optimal topology by considering body forces

Engineering Computations ◽

10.1108/ec-06-2020-0324 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Meisam Takalloozadeh ◽

Gil Ho Yoon

Keyword(s):

Topology Optimization ◽

Level Set ◽

Thermal Loading ◽

Topological Derivative ◽

Optimization Process ◽

Optimal Topology ◽

Content Type ◽

Body Forces ◽

Applied Forces ◽

Level Set Approach

Purpose Body forces are always applied to structures in the form of the weight of materials. In some cases, they can be neglected in comparison with other applied forces. Nevertheless, there is a wide range of structures in civil and mechanical engineering in which weight or other types of body forces are the main portions of the applied loads. The optimal topology of these structures is investigated in this study. Design/methodology/approach Topology optimization plays an increasingly important role in structural design. In this study, the topological derivative under body forces is used in a level-set-based topology optimization method. Instability during the optimization process is addressed, and a heuristic solution is proposed to overcome the challenge. Moreover, body forces in combination with thermal loading are investigated in this study. Findings Body forces are design-dependent loads that usually add complexity to the optimization process. Some problems have already been addressed in density-based topology optimization methods. In the present study, the body forces in a topological level-set approach are investigated. This paper finds that the used topological derivative is a flat field that causes some instabilities in the optimization process. The main novelty of this study is a technique used to overcome this challenge by using a weighted combination. Originality/value There is a lack of studies on level-set approaches that account for design-dependent body forces and the proposed method helps to understand the challenges posed in such methods. A powerful level-set-based approach is used for this purpose. Several examples are provided to illustrate the efficiency of this method. Moreover, the results show the effect of body forces and thermal loading on the optimal layout of the structures.

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Topology optimization of structures subject to self-weight loading under stress constraints

Engineering Computations ◽

10.1108/ec-06-2021-0368 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Renatha Batista dos Santos ◽

Cinthia Gomes Lopes

Keyword(s):

Topology Optimization ◽

Stress Constraints ◽

Topological Derivative ◽

The Self ◽

Von Mises Stress ◽

Stress Constraint ◽

Content Type ◽

Derivative Method ◽

Von Mises ◽

Weight Loading

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

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