Robust topology optimization of structures with uncertainties in stiffness – Application to truss structures

Asadpoure, Alireza; Tootkaboni, Mazdak; Guest, James K.

doi:10.1016/j.compstruc.2010.11.004

Cited by 186 publications

(107 citation statements)

References 20 publications

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“…A key focus of the authors has been in developing intrusive methods that couple the uncertainty quantification with the design sensitivity analysis. These have included the use of perturbation (Guest and Igusa, 2008;Asadpoure et al, 2011) and Polynomial Chaos expansion (Tootkaboni et al, 2012) to optimize structures that are robust in the presence of uncertainty. The robust formulation replaces a deflection metric, for example, with a probabilistic formulation composed of the expected (mean) value of the deflection plus the standard deviation of deflection as follows:…”

Section: Design Under Uncertaintymentioning

confidence: 99%

Structural Topology Optimization: Moving Beyond Linear Elastic Design Objectives

Guest

Lotfi

Gaynor

et al. 2012

20th Analysis and Computation Specialty Conference

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Topology optimization is a systematic, free-form approach to the design of structures. It simultaneously optimizes material quantities and system connectivity, enabling the discovery of new, high-performance structural concepts. While powerful, this design freedom has a tendency to produce solutions that are unrealizable or impractical from a structural engineering perspective. Examples include overly complex topologies that are expensive to construct and ultra-slender subsystems that may be overly susceptible to imperfections. This paper summarizes recent tools developed by the authors capable of mitigating these shortcomings through consideration of (1) constructability, (2) nonlinear mechanics, and (3) uncertainties.

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Section: Design Under Uncertaintymentioning

confidence: 99%

Structural Topology Optimization: Moving Beyond Linear Elastic Design Objectives

Guest

Lotfi

Gaynor

et al. 2012

20th Analysis and Computation Specialty Conference

Self Cite

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“…Bendsøe and Kikuchi presented a method which makes the optimal shape design as the material distribution problem based on the theory of homogenization (Bendsøe and Kikuchi, 1988;Bendsøe, M. P. 1989). In addition, there is another research branch such as incorporating uncertainties into structural topology optimization (Guest et al, 2008;Asadpoure et al, 2011;Chen et al, 2011;Jung et al, 2004;Schevenels et al, 2011;Xu et al, 2016;Xu et al, 2015). The method that we proposed in this article is to resist the structural local failure that may be caused by those uncertainties or possible structural fatigue.…”

Section: Introductionmentioning

confidence: 99%

Continuum Structural Layout in Consideration of the Balance of the Safety and the Properties of Structures

Wang

Liu

Qian

et al. 2017

Lat. Am. j. solids struct.

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In the article, a new approach considering structural local failure for topology optimization of continuum structure is proposed. It aims at not only lowering the risk of local failure in the concerned structural regions, but also ensuring a good stiffness of the structure. The local failure may be caused by the structural uncertainties or possible structural fatigue. To this end, a criterion to evaluate the effect of one local failure on the structure is introduced. This criterion is minimized to reduce the probability of structural damage based on an initialized structure whose compliance is optimized. Solid Isotropic with Material Penalization (SIMP) method and Optimality Criteria (OC) method are combined to solve the design problem. The effectiveness of the proposed algorithm is verified by a series of numerical examples. Furthermore, experiments merging with additive manufacturing technique are taken to prove the practical ability of the method in actual engineering.

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“…The effects of geometric uncertainty were estimated using second order stochastic perturbation and uncertainties in the stiffness of the structure were transformed into a mathematically equivalent system of auxiliary loads. This technique is extended for nonlinear effects of global instability [9] and material property uncertainties [2], to put more control on the variability of the ?nal design via including variance of the compliance [3]. Asadpoure et al [3] present a computational strategy that combines deterministic topology optimization techniques with a perturbation method for the quantification of uncertainties associated with structural stiffness, such as uncertain material properties and/or structure geometry.…”

Section: Introductionmentioning

confidence: 99%

“…This technique is extended for nonlinear effects of global instability [9] and material property uncertainties [2], to put more control on the variability of the ?nal design via including variance of the compliance [3]. Asadpoure et al [3] present a computational strategy that combines deterministic topology optimization techniques with a perturbation method for the quantification of uncertainties associated with structural stiffness, such as uncertain material properties and/or structure geometry. The applied technique leads to significant computational savings when compared with Monte Carlo-based optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

SIMP type topology optimization procedure considering uncertain load position

Lógó

2012

Per. Pol. Civil Eng.

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IntroductionThe topology optimization has more than 100 years of history and still it is an expanding field in structural optimization. The numerical procedure for FE (finite element) based topology optimization of continuum type of structures was elaborated first by Rossow and Taylor [19] in 1973, but the real expansion started at the end of 80-s [4,20]. The majority of the papers still deal with deterministic problems. During these years several optimal topologies were numerically calculated but the analytical confirmations -which have come recently (Rozvany [21], Sokółet. al [22]) -are mostly missing. Until the end of the last century almost one could not find any publication on topology optimization considering uncertainties.During the last years before the millennium almost there were no publications in the topic of probability based topology optimization. The stochastic optimization works of Marti and Stöckl [16,17] provide early information about this topic. The paper of Duan et al. [5] is among the very first publications in the field of uncertainty based topology optimization. This work presents an entropy-based topological optimization method for truss structures by the use of iteration technique. Also a truss topology optimization (layout optimization) of the object of the paper of Alvarez and Carrasco [1] in case stochastic loading. They showed mathematically that a problem of finding the truss of minimum expected compliance (stability of the members are not considered) under stochastic loading conditions is equivalent to the dual of a special convex minimax problem. Dunning et al. [6,7] introduce an efficient and accurate approach to robust structural topology optimization for continuum type of problems. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level-set-based topology optimization method are then used to demonstrate the proposed approach.Topology optimization with uncertainty in the magnitude and

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Robust topology optimization of structures with uncertainties in stiffness – Application to truss structures

Cited by 186 publications

References 20 publications

Structural Topology Optimization: Moving Beyond Linear Elastic Design Objectives

Structural Topology Optimization: Moving Beyond Linear Elastic Design Objectives

Continuum Structural Layout in Consideration of the Balance of the Safety and the Properties of Structures

SIMP type topology optimization procedure considering uncertain load position

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