Stress-based topology optimization for continua

Le, Chau H.; Norato, Julián A.; Bruns, T. E.; Ha, Christopher; Tortorelli, Daniel A.

doi:10.1007/s00158-009-0440-y

Cited by 627 publications

(445 citation statements)

References 34 publications

Supporting

Mentioning

436

Contrasting

Unclassified

Order By: Relevance

“…SIMP was initially introduced by Bendsøe [3] and the name was later suggested by Rozvany [24]. A similar formulation is also used to penalize stresses, as described in Le et al [20] and shown in Section 4 in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, stress constraints were earlier used in optimization of trusses by Dorn et al [12]. In recent years, stress constraints have received attention from Svanberg and Werme [27], Le et al [20] and Paris et al [21] among others. It is noted that, compared to the traditional stiffness maximization problem, additional difficulties occur: Sved and Ginos [28] found that stress constraints are violated as the bar area goes to zero in a truss optimization problem and the bar can thus not be removed (known as singularity).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

336

167

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

336

167

View full text Add to dashboard Cite

show abstract

“…where r N N u is obtained by solving the adjoint state Equation (16) and N N n v ; r vm;ad is given in Equation (17b).…”

Section: One Order Derivative Formula Of the Aggregation Stress Gradimentioning

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%

“…The technique of 'block aggregation' [21] by using more global constraints to reduce the number of constraints involved in a single global function would be helpful in avoiding these disadvantages, but not completely. The adaptive normalization scheme proposed by Le et al [16] works well in controlling the maximum stress. 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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Rong

Xiao

et al. 2016

Numerical Meth Engineering

View full text Add to dashboard Cite

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.

show abstract

Bibliography

2014

Computational Design of Lightweight Structures

View full text Add to dashboard Cite

Stress-based topology optimization for continua

Cited by 627 publications

References 34 publications

Stress constrained topology optimization

Stress constrained topology optimization

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

Bibliography

Contact Info

Product

Resources

About