Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set

Deng, Shiguang; Suresh, Krishnan

doi:10.1007/s00158-017-1732-2

Cited by 49 publications

(14 citation statements)

References 52 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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“…The sandwich panel is covered by two layers of non-designable skins Ω nd on the top and bottom sides. The skins are functioning sealing and withstanding certain external thermo-mechanical loads, such as hot exhaust gases [10,13,15,66]. The core layer is the design domain Ω d , where a reasonabledesigned configuration serves with multiple functions, such as supporting and heat insulation [67].…”

Section: Planar Sandwich Panelmentioning

confidence: 99%

“…In these frameworks, the min-max stress is set as the objective function or the max stress is constrained with a minimum volume. This can be seen as a strength design, such as Refs [13][14][15]. In the work of Deng and Suresh [16] and Wu et al [17], the thermal stress influence on the structural buckling performance is further studied.…”

Section: Introductionmentioning

confidence: 99%

Shape preserving design of thermo-elastic structures considering geometrical nonlinearity

Zhu

Wang

et al. 2020

Struct Multidisc Optim

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“…18 Different TOs with thermo-elastic buckling or stress constraint were presented by means of topological sensitivity. [19][20][21] Deaton and Grandhi 22 considered TO with stress constraint in uniform temperature field and Takezawa et al 23 carried out TO under stress and heat conduction constraints. Recently, Zhu et al 24 proposed the thermo-mechanical TO considering temperature constraint.…”

Section: Introductionmentioning

confidence: 99%

Thermo‐elastic topology optimization with stress and temperature constraints

Meng

Wang

et al. 2021

Numerical Meth Engineering

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A thermo-elastic topology optimization with stress and temperature constraints is proposed to attack the complex multiphysics problem in this paper. Based on the rational approximation of material properties (RAMP), the coupled equations of mechanic and temperature field are solved. Two optimization problems, volume minimization with temperature and stress constraints, and traditional compliance minimization with volume and temperature constraints, are discussed for comparison. The stress stabilizing control scheme (SSCS) combined with global stress measure is presented to tackle highly nonlinear and local nature of stress with thermal expansion in varying temperature field. The adjoint method is applied to achieve the sensitivity of multiphysics field and the density function is updated utilizing the method of moving asymptotes (MMA).Representative examples are investigated to demonstrate the effectiveness and utility of the proposed method. Clear topology and stable iterative process can be obtained for complex coupled problem by means of the SSCS. Meanwhile, the topology with stress and temperature constraints has obvious sensitivity to even subtle change in temperature. The optimization design considering several stress constraints under multithermal conditions can work well in different temperature ranges.

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Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set

Cited by 49 publications

References 52 publications

An accurate and fast regularization approach to thermodynamic topology optimization

An accurate and fast regularization approach to thermodynamic topology optimization

Shape preserving design of thermo-elastic structures considering geometrical nonlinearity

Thermo‐elastic topology optimization with stress and temperature constraints

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