A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints

Guo, Xu; Cheng, Gengdong; Yamazaki, Koetsu

doi:10.1007/s00158-001-0156-0

Cited by 94 publications

(37 citation statements)

References 16 publications

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“…1 Simple example used in [13] to a stress with a nonzero and sometimes remarkably high value, when it actually should be zero as it represents a hole. The singularity problem is discussed in many papers, such as [15], [18], [23] among others, and one way to avoid it is to use an ǫ-relaxation approach as suggested by Cheng and Guo [9] and as is used in stress constrained problems by Duysinx and Bendsøe [13] and Duysinx and Sigmund [14]. We use a stress penalization introduced by Bruggi [7], that besides giving further penalization of intermediate design variables also avoids the singularity problem.…”

Section: Introductionmentioning

confidence: 99%

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

336

167

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This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements.The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.

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Section: Introductionmentioning

confidence: 99%

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

336

167

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“…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%

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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“…However, the method sometimes generates an inaccurate solution for problem with stress and/or local buckling constraints (7), (9) , because these local constraints need not be satisfied by a non-existing member;…”

Section: Introductionmentioning

confidence: 99%

“…The cross-sectional areas for this approximate solution are shown in Table 7. Table 7 Cross-sectional areas for locally optimal braces brace i-j Cross-sectional areas [mm 2 ] 3-11 (5)(6)(7)(8)(9)(10)(11) 719.7 4-10(4-12) 698.1 10-18 (12)(13)(14)(15)(16)(17)(18) 633.7 11-17 (11)(12)(13)(14)(15)(16)(17)(18)(19) 667.9 18-24 (18)(19)(20)(21)(22)(23)(24)(25)(26) 580. 8 We carried out TM and TS with different parameter values.…”

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confidence: 99%

Topology Mining for Optimization of Framed Structures

Hagishita

Ohsaki

2008

JAMDSM

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A new heuristic method called Topology Mining (TM) is proposed for topology optimization of framed structures, where the problem is formulated as 0-1 mixed-integer optimization problem. TM uses the apriori algorithm, developed in the field of data mining, to efficiently extract the bar sets that frequently appears among superior solutions, and proceeds so as to preserve the sets. Hence, the process of optimization can be investigated by tracing the frequent bar sets, accordingly, the parameters for optimization can easily be adjusted. It is pointed out that the ground structure method based on nonlinear programming is not effective for finding optimal placement of braces for a given frame under local buckling constraints. We propose an integrated approach to obtain an accurate solution of this problem, where optimal placement of braces is searched by TM, and the sizing optimization is performed by nonlinear programming. Three numerical examples are solved to demonstrate the performance of TM in comparison with another heuristic method called tabu search.

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A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints

Cited by 94 publications

References 16 publications

Stress constrained topology optimization

Stress constrained topology optimization

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

Topology Mining for Optimization of Framed Structures

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