Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques

Mogami, Katsuya; Nishiwaki, Shinji; Izui, Kazuhiro; Yoshimura, Masataka; Kogiso, Nozomu

doi:10.1007/s00158-006-0039-5

Cited by 65 publications

(38 citation statements)

References 28 publications

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“…refs. [19][20][21][22][23][24][25][26][27]). For truss structures, uncertainties of nodal positions [28,29] as well as failure of individual bars [28] have been considered, but otherwise, uncertain properties have so far been limited to global variables like load magnitude and direction, overall dimensions and material properties, most probably due to the heavy computational cost associated with the inclusion of even a few non-deterministic design variables.…”

Section: Introductionmentioning

confidence: 99%

Manufacturing tolerant topology optimization

2009

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In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under-and over-etching is modelled by image processing-based "erode" and "dilate" operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of onenode connected hinges in compliant mechanism design using topology optimization.

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Section: Introductionmentioning

confidence: 99%

Manufacturing tolerant topology optimization

2009

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“…Equations (3) and (4) state the procedure of RBTO as a nested analysis. The use of PMA to evaluate the probability constraints has been widely accepted as a more efficient calculation method compared to using RIA (Mogami et al (12) ).…”

Section: Formulation Of Rbtomentioning

confidence: 99%

“…On the other hand, the current study is able to adjust multiple penalties for a system reliability problem through an optimization procedure as indicated in Eq. (12). Please note that any general reliability analysis methods can be implemented with Eq.…”

Section: Journal Of Advanced Mechanical Design Systems and Manufactmentioning

confidence: 99%

“…Please note that any general reliability analysis methods can be implemented with Eq. (12). That is, the proposed algorithm allows more accurate methods, including MCS, to be used for reliability analysis for highly nonlinear probabilistic constraints.…”

Section: Journal Of Advanced Mechanical Design Systems and Manufactmentioning

confidence: 99%

“…One way to avoid the reliability analysis in the inner loop is the single-loop approach. Mogami et al (12) have summarized many single-loop approaches to solve reliability-based design optimization (RBDO) problems, such as the Single Loop Single Variable (SLSV) method and the Safety-Factor Approach (SFA). All of these approaches have been successfully developed to avoid having to calculate the reliability index during the optimization process.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Iterative Topology Optimization Algorithm That Considers Randomness in Design Parameters

Liao

2012

JAMDSM

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Topology optimization often incorporates a reliability analysis to take the randomness in the design parameters into account. This strategy is inherently a double-loop procedure due to the probabilistic constraints in optimization. To simplify the calculation procedure, an equivalent-deterministic constraint, which is constructed by adding a penalty on the right hand side (RHS) of a limit state function, is used to reformulate a reliability-based topology optimization (RBTO) problem into a deterministic topology optimization (DTO) problem. To obtain a converged solution, the DTO and the search of equivalent-deterministic constraints must be executed iteratively. The accuracy and efficiency of the proposed approach are investigated through several numerical examples. Results indicated that the proposed algorithm is able to deliver an optimal topology with predefined reliability. Furthermore, one can incorporate the proposed algorithm with existing software to facilitate the design process.

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Robust geometry and topology optimization of plane frames using order statistics and force density method with global stability constraint

Shen

Ohsaki

Yamakawa

2021

Numerical Meth Engineering

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This paper presents a worst case approach for robust geometry and topology optimization of plane frames with global stability constraint. Uncertainty is assumed to exist in the nodal locations and cross‐sectional areas, and the worst values of the objective and stability constraint functions are relaxed to the quantile structural responses represented by the order statistics with given robustness and confidence levels. In order to alleviate the difficulty caused by melting nodes to some extent, the force density method is applied to an auxiliary truss model for geometry optimization of the frame, and the closely spaced nodes are merged. A method is presented for generating correlated imperfections for the nodal locations along each member, and a penalization approach is proposed for geometrical stiffness matrix to exclude superficial local buckling. It is demonstrated in the numerical examples that the result of robust optimization obtained by the proposed method is less sensitive to the uncertainty, and the stability constraint is also satisfied under uncertainty with the specified robustness and confidence levels.

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Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques

Cited by 65 publications

References 28 publications

Manufacturing tolerant topology optimization

Manufacturing tolerant topology optimization

An Iterative Topology Optimization Algorithm That Considers Randomness in Design Parameters

Robust geometry and topology optimization of plane frames using order statistics and force density method with global stability constraint

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