Stress-related topology optimization via level set approach

Gao, Xu; Zhang, Wei Sheng; Wang, Michael Yu; Peng, Wei

doi:10.1016/j.cma.2011.08.016

Cited by 149 publications

(61 citation statements)

References 26 publications

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“…The stress concentration factors of some typical structures, such as components with U-notches and V-notches, are evaluated in structural engineering. There also are the highly nonlinear behavior of the design variables in the aggregation functions, such as the p-norm and the segregated global stress norms [13,[20][21][22][23][24], except this nonlinear behavior caused by the stress concentrations.…”

Section: An Approximation Expressions Of Stress Gradientsmentioning

confidence: 99%

“…Optimal design of the L-shape beam problem under the volume minimum formulation with a compliance constraint and a stress constraint for the full density material with an allowable von Mises stress limit e Y D 70 and the corresponding stress distribution in Ref. [24]. And its optimal design volume is 0.2086. outer loop iterative step.…”

Section: A L-shape Beam Designmentioning

confidence: 99%

“…The corresponding stress distribution of the topology obtained becomes more uniform Optimal design of the L-shape beam problem under a compliance minimum formulation with a volume constraint limit 0.2 and a stress constraint for the full density material with an allowable von Mises stress limit e Y D 70 and the corresponding stress distribution in Ref. [24].…”

Section: A L-shape Beam Designmentioning

confidence: 99%

“…Here, the MMA expression Q f r T C;M .¡/ of f r T C .¡/ with respect to topology variables y v D n v ; v D 1; 2; : : : ; Q at .k 1/ n v ; v D 1; 2; : : : ; Q is adopted and can be given as Equation (24 …”

Section: Explicit Approximations Of Aggregation Functionsmentioning

confidence: 99%

“…However, it is difficult to obtain the exact optimal solution because this scheme may prevent the local stresses of some elements to reach the permissible strength limit. Recently, some remedies [22][23][24] addressed the highly nonlinear behavior including stress concentration issue of the aggregation stress constraints.…”

Section: Introductionmentioning

confidence: 99%

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Continuum structural topological optimizations with stress constraints based on an active constraint technique

Rong

Xiao

et al. 2016

Numerical Meth Engineering

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SUMMARYStress-related problems have not been given the same attention as the minimum compliance topological optimization problem in the literature. Continuum structural topological optimization with stress constraints is of wide engineering application prospect, in which there still are many problems to solve, such as the stress concentration, an equivalent approximate optimization model and etc. A new and effective topological optimization method of continuum structures with the stress constraints and the objective function being the structural volume has been presented in this paper. To solve the stress concentration issue, an approximate stress gradient evaluation for any element is introduced, and a total aggregation normalized stress gradient constraint is constructed for the optimized structure under the r th load case. To obtain stable convergent series solutions and enhance the control on the stress level, two p-norm global stress constraint functions with different indexes are adopted, and some weighting p-norm global stress constraint functions are introduced for any load case. And an equivalent topological optimization model with reduced stress constraints is constructed,being incorporated with the rational approximation for material properties, an active constraint technique, a trust region scheme, and an effective local stress approach like the qp approach to resolve the stress singularity phenomenon. Hence, a set of stress quadratic explicit approximations are constructed, based on stress sensitivities and the method of moving asymptotes. A set of algorithm for the one level optimization problem with artificial variables and many possible non-active design variables is proposed by adopting an inequality constrained nonlinear programming method with simple trust regions, based on the primal-dual theory, in which the non-smooth expressions of the design variable solutions are reformulated as smoothing functions of the Lagrange multipliers by using a novel smoothing function. Finally, a twolevel optimization design scheme with active constraint technique, i.e. varied constraint limits, is proposed to deal with the aggregation constraints that always are of loose constraint (non active constraint) features in the conventional structural optimization method. A novel structural topological optimization method with stress constraints and its algorithm are formed, and examples are provided to demonstrate that the proposed method is feasible and very effective.

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Section: An Approximation Expressions Of Stress Gradientsmentioning

confidence: 99%

Section: A L-shape Beam Designmentioning

confidence: 99%

Section: A L-shape Beam Designmentioning

confidence: 99%

Section: Explicit Approximations Of Aggregation Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Rong

Xiao

et al. 2016

Numerical Meth Engineering

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show abstract

References

2019

Topology Optimization Design of Heterogeneous Materials and Structures

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Optimal topology design of continuum structures with stress concentration alleviation via level set method

Zhang

Guo

Wang

et al. 2012

Numerical Meth Engineering

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SUMMARY Although the phenomenon of stress concentration is of paramount importance to engineers when they are designing load‐carrying structures, stiffness is often used as the solely concerned objective or constraint functional in the studies of optimal topology design of continuum structures. Sometimes this will lead to optimal designs with severe stress concentrations that may be highly responsible for the fracture, creep, and fatigue of structures. The aim of the present work is to develop some effective numerical techniques for designing stiff structures with less stress concentrations. This is achieved by introducing some specific stress measures, which are sensitive to the existence of high local stresses, in the problem formulation and resolving the corresponding optimization problem numerically in a level set framework. Our study indicates that with use of the proposed numerical schemes, some intrinsic difficulties in stress‐related topology optimization of continuum structures can be overcome in a natural way. Copyright © 2012 John Wiley & Sons, Ltd.

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Stress-related topology optimization via level set approach

Cited by 149 publications

References 26 publications

Continuum structural topological optimizations with stress constraints based on an active constraint technique

Continuum structural topological optimizations with stress constraints based on an active constraint technique

References

Optimal topology design of continuum structures with stress concentration alleviation via level set method

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