A Variance-Expected Compliance Model for Structural Optimization

Carrasco, Miguel; Ivorra, Benjamín; Ramos, Ángel

doi:10.1007/s10957-011-9874-7

Cited by 24 publications

(24 citation statements)

References 24 publications

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“…This can also be deduced by observing the shape of both solutions (see Figures 3-4): the density distribution ρ sp is concentrated in the X-Z plane including f , producing a good resistance to the main load, whereas ρ ec exhibits four pillars resilient to the perturbed loads included in the X-Y plane orthogonal to f . From this preliminary result, as in the truss optimization case studied in [7], we can deduce that considering formulation (10) for topology optimization can help to generate structures robust to perturbations of the main load.…”

Section: Resultsmentioning

confidence: 74%

“…We have adapted an expected compliance formulation, coming from truss design (see [3,7]), to topology optimization. We have exhibited, in a particular case, an explicit expression easy to evaluate.…”

Section: Discussionmentioning

confidence: 99%

“…Here, our purpose is to find the optimal distribution of material ρ when the external load force has a stochastic behavior. In an analogous way to previous stochastic results for truss optimization (see [3,7]), we assume that the external load force f is randomly perturbed by ξ , with IE(ξ ) = 0 . The stochastic topology design problem can be stated as min…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An expected compliance model based on topology optimization for designing structures submitted to random loads

Carrasco¹,

Ivorra²,

Lecaros³

et al. 2012

Differential Equations &Amp; Applications

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Abstract. In this paper, we focus in developing a stochastic model for topology optimization. The principal objective of such a model is to find robust structures for a given main load having a stochastic behavior. In the first part, we present the expected compliance formulation and some results in topology optimization. Then, in order to illustrate the interest of our approach, we consider a preliminary 3D cantilever benchmark experiment and compare the obtained results with the one given by a single load approach.

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Section: Resultsmentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An expected compliance model based on topology optimization for designing structures submitted to random loads

Carrasco¹,

Ivorra²,

Lecaros³

et al. 2012

Differential Equations &Amp; Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…In an analogous way to previous stochastic results for truss optimization (see [8,9,10] and the next section), we assume that the external load force…”

Section: Remark 1 In This Work It Is Possible To Include Functions Lementioning

confidence: 99%

“…In other direction, Allaire (see [13]) proposes a deterministic method for optimizing a structure with respect to its worst possible behavior. Similarly to the case of trusses (see [10]) this approach provides solutions which are robust under load perturbations, but for some particular scenarios it may happen that the value of the compliance is too large and this model is no suitable. In order to avoid this situation we propose the following alternative.…”

Section: Remark 2 Similarly Whenmentioning

confidence: 99%

Stochastic topology design optimization for continuous elastic materials

Carrasco

Ivorra

Ramos

2015

Computer Methods in Applied Mechanics and Engineering

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In this paper, we develop a stochastic model for topology optimization. We find robust structures that minimize the compliance for a given main load having a stochastic behavior. First, we give some properties about the stability of structures carrying several loads. Then, we propose a stochastic model that takes into account the expected value of the compliance and its variance. We show that, similarly to the case of truss structures, these values can be computed with an equivalent deterministic approach and the stochastic model can be transformed into a nonlinear programming problem, reducing the complexity of this kind of problems. Finally, we check our formulation by considering several 2D and 3D numerical examples. benchmark case, we consider a set of optimization problems based on different weight coefficients of the compliance, expected-compliance and variance values and compare the robustness of the obtained solutions between them. We see that considering our methodology with an appropriate set of weight coefficients may help to generate structures robust to main loads and their perturbations.

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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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A Variance-Expected Compliance Model for Structural Optimization

Cited by 24 publications

References 24 publications

An expected compliance model based on topology optimization for designing structures submitted to random loads

An expected compliance model based on topology optimization for designing structures submitted to random loads

Stochastic topology design optimization for continuous elastic materials

Robust topology optimization based on finite strain considering uncertain loading conditions

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