Topology Optimization of Trusses under Stochastic Uncertainty

Stöckl, Gerald

doi:10.1002/zamm.200108115124

Cited by 7 publications

(3 citation statements)

References 6 publications

(1 reference statement)

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“…Generally, the papers mirror deterministic problems and only recent publications have integrated the reliability analysis into the deterministic topology optimization problem by the introduction of the reliability constraint into the standard SIMP procedure (Kharmada et al, 2004;Melchers, 2001). Stöckl (2001Stöckl ( , 2003 used the mathematical programming as numerical tool for the solution procedure of different types of stochastic problems in mechanics.…”

Section: Introductionmentioning

confidence: 99%

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#

Lógó

2007

Mechanics Based Design of Structures and Machines

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The aim of this paper is to introduce a new type of stochastic optimal topology design method where the loads are given randomly. The standard stochastic mathematical programming problem is based on penalized minimum weight design procedure subjected to a probabilistic compliance constraint due to the loading uncertainties. If the probability of the compliance constraint is given by the use of recommendation of Prekopa this probabilistic expression can be substituted with an equivalent one and used as a deterministic constraint in the original problem. In the numerical method, optimality criteria procedure is applied. The application is illustrated by numerical examples.

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Section: Introductionmentioning

confidence: 99%

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#

Lógó

2007

Mechanics Based Design of Structures and Machines

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“…There is a rich literature on various applications of reliabilitybased design, and the reader is referred to Tsompanakis et al [25] for a recent collection of state-of-the-art papers, Schueller and Jensen [26] for an excellent review on the recent advance ments on design under uncertainty, and Igusa and Der Kiureghian [27] for a review in dynamics problems and the importance of con sidering randomness in structural characteristics. Specifically in the context of structural topology optimization, a significant amount of work has considered RBTO under uncertainty in loading for structures defined on truss [28] and continuum [29] domains.…”

Section: Introductionmentioning

confidence: 99%

Reliability-based topology optimization of trusses with stochastic stiffness

2013

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NOTICE: this is the author’s version of a work that was accepted for publication in Structural Safety. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Structural Safety, 43, ( July 2013) DOI:10.1016/j.strusafe.2013.02.003 This Article is brought to you for free and open access by the Civil and Environmental Engineering at EngagedScholarship@CSU. It has been accepted for inclusion in Civil and Environmental Engineering Faculty Publications by an authorized administrator of EngagedScholarship@CSU. For mor

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“…Some of the most significant results related to the problem to be solved in this work can be summarized as follows: introduction of stochastic analysis methods for engineering problems including probabilistic finite element methods and random process and field models [21][22][23][24][25]; extension of RBO capabilities upward into the design variable hierarchy, such as shape, material, and topological optimization: sizing [26,27], shape [28][29][30], topology [31][32][33]. Moreover, the direct solution of the structural response and the dynamic reliability when considering the randomness from both the structural parameters and external dynamic loads are very difficult.…”

Section: Introductionmentioning

confidence: 99%

Reliability-based optimization of trusses with random parameters under dynamic loads

Wriggers

Gao

et al. 2011

Comput Mech

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In this work, a reliability-based optimization technique is addressed to obtain the minimum mean value of random mass of the structures with random parameters under stationary stochastic process excitation. The challenge of the problem lies in randomness involved from both structural parameters and dynamic load, which renders the structural reliability becoming the random dynamic reliability of the first passage problem. In order to obtain minimum mean value of random gross mass, element and system dynamic reliability constraints are constructed, respectively, and the structural sizing and shape optimization models based on the dynamic reliability are then presented. Moreover, among two optimal strategies proposed for optimization models, the second one can effectively reduce the workload by avoiding the computation of the variance of the dynamic response during the iterative process. Finally, the implementation of three examples is discussed to display the feasibility and validity of optimization technique given.

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Topology Optimization of Trusses under Stochastic Uncertainty

Cited by 7 publications

References 6 publications

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#

Reliability-based topology optimization of trusses with stochastic stiffness

Reliability-based optimization of trusses with random parameters under dynamic loads

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Topology Optimization of Trusses under Stochastic Uncertainty

Cited by 7 publications

References 6 publications

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions#

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions#

Reliability-based topology optimization of trusses with stochastic stiffness

Reliability-based optimization of trusses with random parameters under dynamic loads

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Product

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New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#

New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#