Structural reliability optimization using an efficient safety index calculation procedure

Wang, Liping; Grandhi, Ramana V.; Hopkins, Dale A.

doi:10.2514/6.1994-1416

Cited by 14 publications

(20 citation statements)

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“…Two major categories of probabilistic optimization strategies exist in the literature. They are the double-loop method [2,[25][26][27] and the single-loop method [4,[28][29][30][31]. With the double-loop method, the loop of reliability analysis (an iterative procedure) is nested within the loop of optimization.…”

Section: Introductionmentioning

confidence: 99%

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Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

Chen

2004

Journal of Mechanical Design

883

347

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The use of probabilistic optimization in structural design applications is hindered by the huge computational cost associated with evaluating probabilistic characteristics, where the computationally expensive finite element method (FEM) is often used for simulating design performance. In this paper, a Sequential Optimization and Reliability Assessment (SORA) method with analytical derivatives is applied to improve the efficiency of probabilistic structural optimization. With the SORA method, a single loop strategy that decouples the optimization and the reliability assessment is used to significantly reduce the computational demand of probabilistic optimization. Analytical sensitivities of displacement and stress functionals derived from finite element formulations are incorporated into the probability analysis without recurring excessive cost. The benefits of our proposed methods are demonstrated through two truss design problems by comparing the results with using conventional approaches. Results show that the SORA method with analytical derivatives is the most efficient with satisfactory accuracy. * KEY WORDSprobabilistic optimization, structural design, Sequential Optimization and Reliability Assessment, finite element method, analytical derivative

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Section: Introductionmentioning

confidence: 99%

“…computation associated with probabilistic analysis, i.e., the evaluation of probabilistic functions and their derivatives [1][2][3][4]. In probabilistic analysis, the system performance needs to be evaluated repeatedly, to capture its probabilistic characteristics.…”

Section: Introductionmentioning

confidence: 99%

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

Chen

2004

Journal of Mechanical Design

883

347

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“…Equation (13) denotes the system of state equations. In the probability constraint, Equation (14), p j denotes the predetermined level of probability of the constraint violation. In Equation (15), the new probability constraint that regulates the variation of performance function is introduced.…”

Section: Robust Optimal Design Formulationmentioning

confidence: 99%

Development of a simple and efficient method for robust optimization

Jung

Lee

2002

Numerical Meth Engineering

113

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SUMMARYRobust optimization problems are newly formulated and an e cient computational scheme is proposed. Both design variables and design parameters are considered as random variables about their nominal values. To ensure the robustness of objective performance, we introduce a new performance index bounding the performance together with a constraint limiting the performance variation. The constraint variations are regulated by considering the probability of feasibility. Each probability constraint is transformed into a sub-optimization problem by the advanced ÿrst-order second moment (AFOSM) method for computational e ciency. The proposed robust optimization method has the advantages that the mean value and the variation of the performance function are controlled simultaneously and rationally and the second-order sensitivity information is not required even in case of gradient-based optimization process. The suggested method is examined by solving three examples and the results are compared with those for the deterministic case and those available in the literature.

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“…As well, the allowable stress caused by static load, F in the beam structure cannot exceed 100 MPa. We start optimization with some arbitrary values of height and width [2,5,6]. According to the beam theory [8], the major contribution to the element's von Mises stress comes from bending stress, although transverse shear stress exists.…”

mentioning

confidence: 99%

Structural Optimization of Cantilever Beam in Conjunction with Dynamic Analysis

Zai¹,

Ahmad²,

Lee³

et al. 2011

Journal of the Korean Institute of Gas

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-In this paper, an analytical model of a cantilever beam having a midpoint load is considered for structural optimization and design. This involves creation of the geometry through a parametric study of all design variables. For this purpose, the optimization of the cantilever beam was elaborated in order to find the optimum geometry which minimizes its volume eventually for minimum weight by FEM (finite element method) analysis. Such geometry can be obtained by different combinations of width and height, so that the beam may have the same cross-sectional area, yet different dynamic behavior. So for optimum safe design, besides minimum volume it should have minimum vibration as well. In order to predict vibration, different dynamic analyses were performed simultaneously to identify the resonant frequencies and mode shapes belonging to the lowest three modes of vibration. Next, by introducing damping effects, the tip displacement and bending stress at the fixed end was evaluated under dynamic loads of varying frequency. Investigation of the results clearly shows that only structural analysis is not enough to predict the optimum values of dimension for safe design it must be aided by dynamic analysis as well.

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Structural reliability optimization using an efficient safety index calculation procedure

Cited by 14 publications

References 0 publications

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

Development of a simple and efficient method for robust optimization

Structural Optimization of Cantilever Beam in Conjunction with Dynamic Analysis

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