Minimization of the expected compliance as an alternative approach to multiload truss optimization

Álvarez, Felipe; Carrasco, Miguel

doi:10.1007/s00158-004-0488-7

Cited by 54 publications

(46 citation statements)

References 13 publications

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“…Theorem 3.1 (Alvarez, Carrasco [4]). Let ξ : Ω → IR n be a continuous random variable with mean vector IE(ξ) = 0, and covariance matrix Var(ξ) = P P T with P ∈ IR n×k for some k ≥ 1.…”

Section: Minimization Stochastic Problemmentioning

confidence: 99%

“…Typically, optimal trusses are unstable under load perturbations (see for example [4,8]). Therefore, in order to design robust truss structures it is necessary to include theses perturbations into the model.…”

Section: Introductionmentioning

confidence: 99%

“…Assuming that loads are random variables, Alvarez and Carrasco [4] propose the problem of finding the truss of minimum expected compliance (see problem (D V ar ; IP; α; 0) in Section 3). They show that this problem can be reformulated as a multiload-type problem, but with a different interpretation of the scenarios.…”

Section: Introductionmentioning

confidence: 99%

“…They show that this problem can be reformulated as a multiload-type problem, but with a different interpretation of the scenarios. Since multiload problems can be equivalently formulated as a convex finitedimensional problem, then the expected-compliance model may be efficiently solved, see [3,7,23,9] The stochastic setting given in [4] allows us to consider the minimum variance-compliance problem, where the variance of the compliance is included into the model. This stochastic model is also equivalent to a nonlinear programming problem.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, we present the mathematical formulation of the variance-expected compliance model, based on [4,12]. Finally, in Section 4, the results are analyzed and compared in terms of robustness among them.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Variance-Expected Compliance Model for Structural Optimization

Carrasco

Ivorra

Ramos

2011

J Optim Theory Appl

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Section: Minimization Stochastic Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Variance-Expected Compliance Model for Structural Optimization

Carrasco

Ivorra

Ramos

2011

J Optim Theory Appl

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Robust topology optimization based on finite strain considering uncertain loading conditions

Nishino

Kato

2020

Numerical Meth Engineering

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The present study proposes a method of robust topology optimization assuming uncertainties in the magnitude and direction of loads applied to a geometrically nonlinear structure. The objective function is the sum of the expected value and the standard deviation of end-compliance of a structure with a compressible Neo-Hookean hyperelasticity. In this study, quadratic approximation of the end-compliance with respect to random variables is employed to reduce computational cost. To ensure its accuracy, a complete analytical formulation is derived, and the performance and limitation of the proposed method are deeply discussed. The performance of the proposed method is verified and its numerical examples emphasize the importance of considering geometrical nonlinearity to obtain robust structures with respect to uncertainties of loading conditions. Finally, we have obtained a finding that the optimized network system consisting of thin members plays a significant role in the improvement of robustness of structures.

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On Shape Optimization with Stochastic Loadings

Atwal

Conti

Geihe

et al. 2011

International Series of Numerical Mathematics

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Abstract. This article is concerned with different approaches to elastic shape optimization under stochastic loading. The underlying stochastic optimization strategy builds upon the methodology of two-stage stochastic programming. In fact, in the case of linear elasticity and quadratic objective functional our strategy leads to a computational cost which scales linearly in the number of linearly independent applied forces, even for a large set of realization of the random loading. We consider, besides minimization of the expectation value of suitable objective functionals, also two different risk-averse approaches, namely the expected excess and the excess probability. Numerical computations are performed using either a level-set approach representing implicit shapes of general topology in combination with composite finite elements to resolve elasticity in two and three dimensions, or a collocation boundary element approach, where polygonal shapes represent geometric details attached to a lattice and describing a perforated elastic domain. Topology optimization is performed using the concept of topological derivatives. We generalize this concept, and derive an analytical expression which takes into account the interaction between neighboring holes. This is expected to allow efficient and reliable optimization strategies of elastic objects with a large number of geometries details on a fine scale. Mathematics Subject Classification (2000). 90C15, 74B05, 65N30, 65N38, 34E08, 49K45.Keywords. shape optimization in elasticity, two-stage stochastic programming, risk averse optimization, level set method, boundary element method, topological derivative.

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Minimization of the expected compliance as an alternative approach to multiload truss optimization

Cited by 54 publications

References 13 publications

A Variance-Expected Compliance Model for Structural Optimization

A Variance-Expected Compliance Model for Structural Optimization

Robust topology optimization based on finite strain considering uncertain loading conditions

On Shape Optimization with Stochastic Loadings

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