Stress-constrained shape and topology optimization with the level set method using trimmed hexahedral meshes

Nguyen, Son H.; Kim, Hyun‐Gyu

doi:10.1016/j.cma.2020.113061

Cited by 34 publications

(7 citation statements)

References 39 publications

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“…Topology optimization (TO) is a method of optimizing the design domain structure according to the given load and boundary conditions on the basis of satisfying constraints such as stress, and displacement [1][2][3]. Topology optimization has attracted considerable attention from researchers with major topology optimization methods including: density-based TO methods [4,5], the le vel set method [6,7], the phase field method [8], Moving Morphable Components/Voids (MMC/V) method [9], the bubble method [10], etc. Among them, the density method has obtained considerable discussion.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions

Tran

2023

Eureka: PE

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Topology optimization (TO) has become increasingly popular as a useful tool for designers and engineers during the initial stages of design. TO aims to optimize the geometry of a design to achieve a specific objective, which can range from discrete grid-like structures to continuum structures. In essence, the geometry is parameterized pixel-by-pixel, with the material density of each element or mesh point serving as a design variable. After that, the optimization problem is addressed using mathematical programming and analytic gradient calculation-based optimization approaches. In this paper, we investigate the material distribution when performing topology optimization for an isotropic material with boundary conditions including fixed structures, supports, or external forces changing. In addition, we investigate more cases where there are material holes in the design domain, meaning that the density of the material is zero. In this study, the modified SIMP method and filter sensitivity are used for topology optimization. The results of the study are the optimized structural domains and the change in compliance according to the number of iterations. The results indicate that the compliance value of most structures reaches convergence after optimization up to the 20th iteration. Moreover, if the force applied to the design domain is symmetrical, the optimal structure also exhibits symmetry. Thus, the distribution of material is concentrated at the positions of the supports. Topology optimization produces designs that both meet boundary conditions while saving material and reducing their mass. The results obtained are important data for structural optimization design for isotropic elastomeric materials. From there, it can be applied to real objects with different requirements and conditions

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Section: Introductionmentioning

confidence: 99%

Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions

Tran

2023

Eureka: PE

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“…Beside improving the basics of the method, many engineering optimization problems have also been addressed in recent years. [10][11][12][13][14][15][16][17][18][19] Due to variety of topology optimization applications in real-life engineering problems, the optimization methods frequently face complicated physical domains. This leads to employ irregular discretizing mesh for the computational model of the problem.…”

Section: Introductionmentioning

confidence: 99%

“…Also, Dunning et al 8,9 used the sequential quadratic programming to enhance the level set method for considering multiple optimization constraints. Beside improving the basics of the method, many engineering optimization problems have also been addressed in recent years 10–19 …”

Section: Introductionmentioning

confidence: 99%

A parameter space approach for isogeometrical level set topology optimization

Aminzadeh

Tavakkoli

2022

Numerical Meth Engineering

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In this article, a new isogeometrical level set topology optimization is introduced. In previous studies, the level set function is approximated by b-splines basis functions and the control net is updated during the optimization process. Since control points are not basically on the level set surface, a discrepancy between zero level of function that represents boundaries of the structure, and zero level of its control netis appeared. In this article, the idea is solving level set equation (LSE) over the parameter space of b-splines basis functions defined in the IGA model. Afterwards, the updated level set function is mapped into the physical space. The level set function is approximated over a grid defined in parameter space which is constantly a unit square. By doing so, control net of the IGA model and the grid for solving LSE are separated. Two well-known radial basis functions (RBF) and reaction-diffusion (RD) based methods are employed to solve the LSE. The proposed method is applied to minimize the mean compliance when certain amount of material is used and also for weight minimization subject to local stress constraints. Several numerical examples are presented to demonstrate performance and accuracy of the proposed method.

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“…Since the seminal paper by Duysinx and Bendsøe, 7 several works addressing topology optimization with stress constraints have been developed. Among them, there are works that focus on developing more efficient and accurate ways to handle the stress constraints, [8][9][10][11][12][13][14][15][16] and works that focus on novel applications, [17][18][19][20] as the problem of compliant mechanisms with stress constraints. [21][22][23][24][25][26][27] Although not novel, stress-constrained topology optimization has been the subject of intensive research in the literature up to the present day.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

Silva

Aage

Beck

et al. 2020

Numerical Meth Engineering

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In topology optimization, the treatment of stress constraints for very large scale problems (more than 100 million elements and more than 600 million stress constraints) has so far not been tractable due to the failure of robust agglomeration methods, that is, their inability to accurately handle the locality of the stress constraints. This article presents a three-dimensional design methodology that alleviates this shortcoming using both deterministic and robust problem formulations. The robust formulation, based on the three-field density projection approach, is extended and proved necessary to handle manufacturing uncertainty in three-dimensional stress-constrained problems. Several numerical examples are solved and further postprocessed with body-fitted meshes using commercial software. The numerical investigations demonstrate that: (1) the employed solution approach based on the augmented Lagrangian method is able to handle very large problems, with hundreds of millions of stress constraints; (2) three-dimensional stress-based results are extremely sensitive to slight manufacturing variations; (3) if appropriate interpolation parameters are adopted, voxel-based (fixed grid) models can be used to compute von Mises stresses with excellent accuracy; and (4) in order to ensure manufacturing tolerance in three-dimensional stress-constrained topology optimization, a combination of double filtering and more than three density field realizations may be required.

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Stress-constrained shape and topology optimization with the level set method using trimmed hexahedral meshes

Cited by 34 publications

References 39 publications

Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions

Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions

A parameter space approach for isogeometrical level set topology optimization

Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

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