?-relaxed approach in structural topology optimization

Cheng, Gengdong; Guo, Xu

doi:10.1007/bf01197454

Cited by 432 publications

(180 citation statements)

References 14 publications

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“…Following Svanberg's approach [30], artificial variables w D w 1 ; w 2 ; : : : ; w m T ; w > 0, are introduced into the optimization problem (12), so that the following enlarged problem is addressed. Even if there is an empty solution set for the optimization model (12), a solution with the minimum violating the constraints in Equation (12) can be obtained.…”

Section: A Transferred Approximate Optimization Modelmentioning

confidence: 99%

“…Being referred to the varied constraint limit approach in Refs. [26][27][28], the original optimization model (6) is transferred into the approximate model (12), which replaces the model (10). …”

Section: An Equivalent Topology Optimization Approximate Model With Smentioning

confidence: 99%

“…Moreover, the elements with topology variable min n q D 0:00001 are removed from the optimized structure as the structure shown in Figure 1(b), and the mesh information of this modified optimized structure, are renewed. At the beginning of the consequent iteration steps, the varied aggregation function constraint limits described earlier are changed according to the Equation 13, for the models (12).…”

Section: Heuristic Operation At a Phase Transferring Stepmentioning

confidence: 99%

“…The singularity issue in the STOM indicates that the stress constraints defined at the centers of the finite elements of the void domain should be removed at every iteration of the optimization [6,[12][13][14][15][16]. Many relaxation methods have been proposed to resolve this issue [6,[12][13][14][15][16], in which the qp-relaxation method has been applied owning to its simplicity and effectiveness.…”

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: A Transferred Approximate Optimization Modelmentioning

confidence: 99%

Section: An Equivalent Topology Optimization Approximate Model With Smentioning

confidence: 99%

Section: Heuristic Operation At a Phase Transferring Stepmentioning

confidence: 99%

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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“…From a mathematical point of view, the classical algorithms are unable to reach some optimum configurations because of the degeneracy of the design space. In order to turn around the difficulty, one has to use a perturbation technique of the stress constraints, generally known as the ε-relaxation technique (Cheng and Guo, 1997) that results in a relaxation of the stress limits in the low-density regions. In this paper we use the following ε-relaxed formulation of the overall stress criterion:…”

Section: Stress Constraintsmentioning

confidence: 99%

Recent Progress in Preliminary Design of Mechanical Components with Topology Optimization

Duysinx

Bruyneel

2002

Integrated Design and Manufacturing in Mechanical Engineering

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Topology optimization of continuum structures with local stress constraints

Duysinx

Bendsøe

1998

Int. J. Numer. Meth. Engng.

562

103

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We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We ÿrst consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model that extends the power penalized sti ness model (also called SIMP for Solid Isotropic Microstructure with Penalization for intermediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called 'singularity' phenomenon of stress constraints in topology design, an -constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications. ? 1998 John Wiley & Sons, Ltd.

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?-relaxed approach in structural topology optimization

Cited by 432 publications

References 14 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

Recent Progress in Preliminary Design of Mechanical Components with Topology Optimization

Topology optimization of continuum structures with local stress constraints

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