Abstract
In order to take into account the uncertainties linked to the variables in the evaluation of the statistical properties of structural response, a reliability approach with probabilistic aspect was considered. This is called the Probabilistic Transformation Method (PTM). This method is readily applicable when the function between the input and the output of the system is explicit. However, the situation is much more involved when it is necessary to perform the evaluation of implicit function between the input and the output of the system through numerical models. In this work, we propose a technique that combines Finite Element Analysis (FEA) and Probabilistic Transformation Method (PTM) to evaluate the Probability Density Function (PDF) of response where the function between the input and the output of the system is implicit. This technique is based on the numerical simulations of the Finite Element Analysis (FEA) and the Probabilistic Transformation Method (PTM) using an interface between Finite Element software and Matlab. Some problems of structures are treated in order to prove the applicability of the proposed technique. Moreover, the obtained results are compared to those obtained by the reference method of Monte Carlo. A second aim of this work is to develop an algorithm of global optimization using the local method SQP, because of its effectiveness and its rapidity of convergence. For this reason, we have combined the method SQP with the Multi start method. This developed algorithm is tested on test functions comparing with other methods such as the method of Particle Swarm Optimization (PSO). In order to test the applicability of the proposed approach, a structure is optimized under reliability constraints.
Highlights
As the properties of the realistic structure, the model is necessary to take into account some uncertainty
A fundamental problem in structural reliability analysis is the computation of the probability integral ([1,2,3,4,5]): Pf Prob G X 0 f X dX (1) G X 0 where X X1, X n T in which T is the transpose, is a vector of random variables representing the uncertain parameters of considered structure, f X is the probability density function of X, G X is the Limit State Function defined such that: G X 0 is the domain of integration denoted the failure set, and Pf is the probability of failure
In order to evaluate the performance of the method proposed, we compare the solutions obtained by the MSQP algorithm with the solutions reported in
Summary
As the properties of the realistic structure, the model is necessary to take into account some uncertainty This uncertainty can be conveniently described in terms of probability measures, such as distribution functions. A fundamental problem in structural reliability analysis is the computation of the probability integral ([1,2,3,4,5]): In this paper, a proposed Method: Finite Element Analysis (FEA) coupled with the Probabilistic Transformation Method (PTM) is applied in order to evaluate numerically the probabilistic and statistical characteristics of the response of stochastic mechanical system It involves four main steps: 1) sampling on input random variables; 2) using Finite Element Analysis (FEA) software to have the response variable of system; 3) estimating the Probabilistic Density Function (PDF) of this response variable using the Probabilistic Transformation AM
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