Topology optimization under thermo-elastic buckling

Deng, Shiguang; Suresh, Krishnan

doi:10.1007/s00158-016-1611-2

Cited by 61 publications

(18 citation statements)

References 48 publications

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“…The designed layout optimized for u p = 0.05 shows that the horizontal compression is dominant with the additional small bending due to the vertical force. These optimum layouts also agree well with the layouts obtained via linear compliance minimization in which a cantilever with only central axial load is considered [15]. Adding a temperature does not change the optimum layout of u p = 0.05, although the required mechanical load Fig.…”

Section: Short Cantilever Beamsupporting

confidence: 80%

“…According to these results, it can be therefore concluded that the proposed optimization method produces the slit and struts, which are beneficial in maximizing buckling capacity for the given material volume. The study also helps to understand why slits and struts are found in optimum structures when mechanical buckling load is considered through a linear buckling constraint [59], or randomly imposed geometric imperfections [41]. When the present scheme is incorporated within the multiscale optimization [53], hierarchical lattice-like structures are expected as optima in the small-scale regime [60].…”

Section: Mechanical Loading Onlymentioning

confidence: 91%

“…after linearizing (15) with respect to Ω. The boundary is then discretized by B number of line segments and (16) is reduced to…”

Section: Level-set Topology Optimizationmentioning

confidence: 99%

“…Comparative studies were also conducted by Zhang et al, [12], where the topological layouts resulting either from strain energy minimization or mean compliance minimization are compared and discussed. These lead to a search of alternative thermoelastic merit functions, such as a constraint on local stress concentration [13,14], and a thermoelastic buckling constraint [15].…”

Section: Introductionmentioning

confidence: 99%

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Level-set topology optimization considering nonlinear thermoelasticity

Chung

Kim

2020

Computer Methods in Applied Mechanics and Engineering

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At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.

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Section: Short Cantilever Beamsupporting

confidence: 80%

Section: Mechanical Loading Onlymentioning

confidence: 91%

“…after linearizing (15) with respect to Ω. The boundary is then discretized by B number of line segments and (16) is reduced to…”

Section: Level-set Topology Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Level-set topology optimization considering nonlinear thermoelasticity

Chung

Kim

2020

Computer Methods in Applied Mechanics and Engineering

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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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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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Topology optimization under thermo-elastic buckling

Cited by 61 publications

References 48 publications

Level-set topology optimization considering nonlinear thermoelasticity

Level-set topology optimization considering nonlinear thermoelasticity

An accurate and fast regularization approach to thermodynamic topology optimization

Thermo‐elastic topology optimization with stress and temperature constraints

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