Optimum structural design via convex model superposition

Ganzerli, Sara; Pantelides, Chris P.

doi:10.1016/s0045-7949(99)00077-2

Cited by 90 publications

(26 citation statements)

References 15 publications

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“…Let Âe i = i ; i = 1; 2; : : : ; m then the convex model (12) can also be written in the following simple form:…”

Section: Static Displacement Problem Of Structures With Uncertain-butmentioning

confidence: 99%

“…In the models, all structural and load parameters with uncertainties are assumed to be bounded from above and below. In the frequently encountered case where su cient knowledge about the structural parameters is absent for substantiation of the stochastic analysis, based on a set-theoretic formulation, in recent studies by Ben-Haim and Elishako [1][2][3], Elishako and Qiu [4][5][6][7][8], Chen and Yang [9], Mullen and Muhanna [10], and Pantelides and Ganerli [11][12][13], convex models and interval analysis methods of uncertainty were developed for modelled uncertain parameters of structures, in which bounds on the magnitude of uncertain parameters are only required, not necessarily knowing the probabilistic distribution densities, following the general methodologies developed in the monographs. It was assumed that the structural characteristics fall into the multidimensional ellipsoid or solid ball, instead of the conventional optimization studies, where the minimum possible response is sought, in which an uncertainty modelling is developed as an anti-optimization problem of ÿnding the least favourable response and the most favourable response under the constraints within the set-theoretical description.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of static response of structures using convex models and interval analysis method

Qiu

2003

Numerical Meth Engineering

101

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SUMMARYIn this paper, by combining the ÿnite element analysis and non-probabilistic convex models, we present the numerical algorithm of non-probabilistic convex models and interval analysis method for the static displacement of structures with uncertain-but-bounded parameters. Under the condition of the box or interval vector determined from the ellipsoid of the uncertain-but-bounded structural parameter vector, by comparing the numerical algorithm of non-probabilistic convex models and the interval analysis method in the mathematical proof and the numerical example, we can see that the width of the maximum or upper and minimum or lower bounds on the static displacement yielded by the numerical algorithm of non-probabilistic convex models is tighter than those produced by the interval analysis method.

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“…Let Âe i = i ; i = 1; 2; : : : ; m then the convex model (12) can also be written in the following simple form:…”

Section: Static Displacement Problem Of Structures With Uncertain-butmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of static response of structures using convex models and interval analysis method

Qiu

2003

Numerical Meth Engineering

101

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“…If only incomplete information is available, it is possible to establish the minimum and maximum favorable response of the structures using interval analysis or convex models [5,6]. Moreover structural analysis with interval parameters using interval based approach has been studied by various authors [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics

Behera¹,

Chakraverty²

2013

IJCA

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Fuzzy finite element analysis for static displacements of beam structures with fuzzy forces is considered in this paper. The material properties of the beams are taken as crisp. Fuzzy finite element analysis of static problem for the above structures converts the problem into fuzzy system of linear equations. As such the coefficient matrix and the right hand side vector become crisp and fuzzy respectively. Here, a new method is proposed to solve the fuzzy system of linear equations. Numerical results for the beam structures are presented to illustrate the computational aspects of the developed method. The results obtained by the proposed method are compared with the existing solution method. KeywordsTriangular fuzzy number, Fuzzy system of linear equations, Fuzzy finite element method, Beam.

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“…In order to quantify the non-probabilistic input data various possibilistic structural analysis methods have been developed. In recent studies convex models, interval analysis methods of uncertainty [1][2][3][4][5] and fuzzy set theory based safety evaluations [6][7][8][9][10] were developed. These algorithms mainly tried to explore the entire range of uncertain variables to assess safety.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic safety analysis of structures under hybrid uncertainty

Chakraborty

Sam

2006

Numerical Meth Engineering

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SUMMARYThe probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently. When the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic, available literatures normally start with either probabilistic or possibilistic description of all the variables. This may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system. The primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data. Relying on the fundamental concept of equivalent transformations, i.e. the entropy based transformation and the scaling of fuzzy membership function, the reliability analysis is proposed in the framework of second moment format. In doing so, the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first-order reliability analysis for consistent comparison among alternative transformations. Finally, the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives.

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Optimum structural design via convex model superposition

Cited by 90 publications

References 15 publications

Comparison of static response of structures using convex models and interval analysis method

Comparison of static response of structures using convex models and interval analysis method

Fuzzy Finite Element based Solution of Uncertain Static Problems of Structural Mechanics

Probabilistic safety analysis of structures under hybrid uncertainty

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