Multi-constrained 3D topology optimization via augmented topological level-set

Deng, Shiguang; Suresh, Krishnan

doi:10.1016/j.compstruc.2016.02.009

Cited by 32 publications

(11 citation statements)

References 68 publications

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“…This can be achieved either by tracing the phase borders or by introducing a density field that describes the material configuration in each point of the design space. The phase borders are subject to optimization in level‐set approaches, which became popular recently due to the inclusion of coupled mechanical problems, eg, buckling and thermal induced stresses, and stress and manufacturing constraints . In density field‐based approaches, a discrete density or a continuous density interpolation is introduced.…”

Section: Introductionmentioning

confidence: 99%

An accurate and fast regularization approach to thermodynamic topology optimization

Jantos

Hackl

Junker

2018

Numerical Meth Engineering

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In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme for the spatial distribution of density mass describing the topology. Consequently, no additional mathematical minimization algorithms are needed. In this article, we introduce a regularization scheme by penalization of the gradient of the spatial distribution of mass density. The parabolic evolution equation (owing to a similar structure to the transient heat-conduction equation) is solved most efficiently by an explicit time discretization. The Laplace operator is discretized via a Taylor series expansion yielding an operator matrix that is constant for the entire optimization process. This method shares some similarities to meshless methods and allows for an accurate application also on unstructured finite element meshes. The minimal size of the structure member can directly be controlled, a priori, by a numerical parameter introduced along with the regularization, similar to classical filter radii. KEYWORDSmeshless Laplacian, parabolic PDE, regularization, thermodynamic topology optimization, unstructured meshes, variational material modeling INTRODUCTIONOver recent decades, topology optimization has become a major field of interest in mechanical engineering. Approaches have been developed for different optimization objectives, constraints relating to physically feasible or manufacturable designs, or models for multiphysics problems. The most native approach is considered to be topology optimization with compliance minimization under a structure volume constraint for linear elastic materials, see, eg, the work of Bendsøe and Sigmund, 1 in which the elastic strain energy is subject to minimization and is referred to as (structural) compliance. Numerous solution approaches were developed of which the most popular are overviewed and compared in the work of Sigmund and Maute. 2 Usually, the topology has to be found within a given design space under mechanical boundary conditions, for which the mechanical problem is solved by a finite element approach. The design space contains material and void phases to identify the topology.This can be achieved either by tracing the phase borders or by introducing a density field that describes the material configuration in each point of the design space. The phase borders are subject to optimization in level-set approaches, 3,4 which Int J Numer Methods Eng. 2019;117:991-1017.wileyonlinelibrary.com/journal/nme

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Section: Introductionmentioning

confidence: 99%

An accurate and fast regularization approach to thermodynamic topology optimization

Jantos

Hackl

Junker

2018

Numerical Meth Engineering

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“…7d) showed the maximum stress is 560 MPa by the stress is limited to 600 MPa. Both cases terminated based on criteria in (5) with the stress in the next iteration is over the limit.…”

Section: Investigation For the Over-relaxationmentioning

confidence: 99%

“…Topology optimization problems have been formulated and solved for various linear analysis problem. The structure was determined a final structure based on Solid Isotropic Material with Penalization approach (SIMP) [1,2,3] and level set approach [4,5] by maximizing the stiffness of structure under a volume constraint. Both SIMP and level set methods are a common approach to seek an optimal layout of the structure by requiring sensitivity analysis and level set function for updating the design variable in each iteration, respectively.…”

Section: Introductionmentioning

confidence: 99%

Optimization on mechanical structure for material nonlinearity based on proportional topology method

Kongwat

Hasegawa

2019

JASSE

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Topology optimization is one complex method due to a final layout obtained by an initial shape is not a consideration. This paper purposes a proportional technique to determine an optimal layout by employing the topology optimization method. The objective function is to maximize an internal energy density by stress constraint based on the bi-linear elastoplasticity material properties. Fully stress design criterion is concerned to be a factor of the proportional technique for updating the design variable. Finally, the optimal layout acquires from the proportional technique and results are faster to converge with an over-relaxation factor which applied to the fully stress design.

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“…A popular method for imposing such constraints the augmented Lagrangian method [57], where the constraint and objective are combined to a single field: where m is the Lagrangian multiplier and g is the penalty parameter (that are updated during the optimization process [57]). By taking the topological derivative of Equation (14), we arrive at Equation (15) for the effective sensitivity [58], [59]:…”

Section: Sensitivity Weightingmentioning

confidence: 99%

“…Observe that the resulting field is a combination of the two fields in Figure 11 and Figure 12. As the optimization progresses, the weight is determined dynamically from Equation (15), while the parameters m and g are updated during each iteration as described in [58], [59].…”

Section: Sensitivity Weightingmentioning

confidence: 99%

Support structure constrained topology optimization for additive manufacturing

Mirzendehdel

Suresh

2016

Computer-Aided Design

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260

109

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There is significant interest today in integrating additive manufacturing (AM) and topology optimization (TO). However, TO often leads to designs that are not AM friendly. For example, topologically optimized designs may require significant amount of support structures before they can be additively manufactured, resulting in increased fabrication and clean-up costs.In this paper, we propose a TO methodology that will lead to designs requiring significantly reduced support structures. Towards this end, the concept of "support structure topological sensitivity" is introduced. This is combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints. The robustness and efficiency of the proposed method is demonstrated through numerical experiments, and validated through fused deposition modeling, a popular AM process.

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Multi-constrained 3D topology optimization via augmented topological level-set

Cited by 32 publications

References 68 publications

An accurate and fast regularization approach to thermodynamic topology optimization

An accurate and fast regularization approach to thermodynamic topology optimization

Optimization on mechanical structure for material nonlinearity based on proportional topology method

Support structure constrained topology optimization for additive manufacturing

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