Reliability-based topology optimization of trusses with stochastic stiffness

Jalalpour, Mehdi; Guest, James K.; Igusa, Takeru

doi:10.1016/j.strusafe.2013.02.003

Cited by 58 publications

(26 citation statements)

References 37 publications

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“…truss elements vs continuum elements). For instance, while in the author's previous paper (Jalalpour et al 2013) the response was found to follow a Gumbel distribution for truss structures under uncorrelated nor mally distributed node location uncertainty, in the present work-a continuum structure under correlated lognormally distributed material uncertainties-the response follows a lognormal distribution. To find the appropriate distribu tion.…”

Section: Response Statisticsmentioning

confidence: 40%

“…where C is the covariance matrix of the basic random vari ables, and tr{•} is the trace operator. The variance of the compliance, obtained using a first order estimate of C, can be expressed as (Asadpoure et al 2011;Jalalpour et al 2013):…”

Section: Response Statisticsmentioning

confidence: 99%

“…The solutions to these subproblems can be obtained via fast Cholesky factorization of the matrix K0 once. We therefore, in place of the last terms in (23) and (24), compute: It can be shown (Asadpoure et al 2010;Jalalpour et al 2013) that sensitivities of expected value and variance are of the following forms:…”

Section: Sensitivities With Respect To Design Variablesmentioning

confidence: 99%

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An efficient approach to reliability-based topology optimization for continua under material uncertainty

Jalalpour

Tootkaboni

2015

Struct Multidisc Optim

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This contribution presents a computationally effi cient method for reliability-based topology optimization for continuum domains under material properties uncertainty. Material Young's modulus is assumed to be lognormally distributed and correlated within the domain. The com putational efficiency is achieved through estimating the response statistics with stochastic perturbation of second order, using these statistics to fit an appropriate distribu tion that follows the empirical distribution of the response, and employing an efficient gradient-based optimizer. Two widely-studied topology optimization problems are exam ined and the changes in the optimized topology is dis cussed for various levels of target reliability and correlation strength. Accuracy of the proposed algorithm is verified using Monte Carlo simulation.

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Section: Response Statisticsmentioning

confidence: 40%

Section: Response Statisticsmentioning

confidence: 99%

Section: Sensitivities With Respect To Design Variablesmentioning

confidence: 99%

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An efficient approach to reliability-based topology optimization for continua under material uncertainty

Jalalpour

Tootkaboni

2015

Struct Multidisc Optim

Self Cite

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“…One key aspect of designs obtained by means of optimization is their extreme sensitivity to any change in the parameters considered during optimization. Thus, slight changes in the magnitude and/or direction of the loads or in the distribution of material properties can lead to large changes in the design or in the effective response of the optimized component.…”

Section: Introductionmentioning

confidence: 99%

Robust topology optimization of compliant mechanisms with uncertainties in output stiffness

Cardoso

Silva

Beck

2019

Numerical Meth Engineering

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Summary This work addresses the topology optimization approach to design robust compliant mechanisms with respect to uncertainties in the output stiffness, when compared to the traditional deterministic approach. To this end, two formulations are proposed: probabilistic and nonprobabilistic. The probabilistic formulation minimizes a joint objective function of expected output displacement plus a measure of its standard deviations, for given statistical distribution of the output stiffness. The nonprobabilistic formulation is written as minimization of a joint function of the median of output displacements, plus the width of the intervals that contains the extreme values of the output displacements, for a given interval of output stiffness. The Monte Carlo simulation method is used to evaluate expected values and standard deviations of output displacements in the probabilistic formulation and to assess results obtained with the deterministic approach. It is shown that both formulations lead to designs where output displacements are less sensitive to variations of output stiffness when compared to the traditional deterministic approach. Furthermore, as an additional benefit, it is observed that large variations of output stiffness can hinder the appearance of one‐node connected hinges, usually found in the deterministic design of compliant mechanisms.

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“…In , using maximum allowable displacement as a failure mode and considering the applied load and Young's modulus as random variables, a minimum weight continuum structure is achieved with a decoupled RBDO approach. In , a single‐loop algorithm is proposed to obtain minimum‐volume truss structures with uncertainties in both nodal locations and members' Young's modulus using maximum allowable displacement as a failure mode. In , a comparison between the nested RBDO algorithm (double‐loop) and a sequential RBDO algorithm is performed in structural problems and in a heat conduction problem, where the same results are achieved.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of continuum structures subjected to uncertainties in material properties

Silva

Cardoso

2016

Numerical Meth Engineering

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SUMMARYThis work addresses the use of the topology optimization approach to the design of robust continuum structures under the hypothesis of uncertainties with known second-order statistics. To this end, the second-order perturbation approach is used to model the response of the structure, and the midpoint discretization technique is used to discretize the random field. The objective function is a weighted sum of the expected compliance and its standard deviation. The optimization problem is solved using a traditional optimality criteria method. It is shown that the correlation length plays an important role in the obtained topology and statistical moments when only the minimization of the standard deviation is considered, resulting in more and thinner reinforcements as the correlation length decreases. It is also shown that the minimization of the expected value is close to the minimization of the deterministic compliance for small variations of Young's modulus.

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Reliability-based topology optimization of trusses with stochastic stiffness

Cited by 58 publications

References 37 publications

An efficient approach to reliability-based topology optimization for continua under material uncertainty

An efficient approach to reliability-based topology optimization for continua under material uncertainty

Robust topology optimization of compliant mechanisms with uncertainties in output stiffness

Topology optimization of continuum structures subjected to uncertainties in material properties

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