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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
A Procedure for Structural Reliability Analysis based on Meshless Methods
J.E. Rojas12, F.A.C. Viana2, A. El Hami1 and D.A. Rade2
1Mechanics Laboratory of Rouen, National Institute for Applied Sciences, Rouen, France
J.E. Rojas, F.A.C. Viana, A. El Hami, D.A. Rade, "A Procedure for Structural Reliability Analysis based on Meshless Methods", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 41, 2007. doi:10.4203/ccp.86.41
Keywords: meshless methods, gradient-based methods reliability, heuristic based reliability method.
In computational mechanics, classical mesh-based methods encounter difficulties in the simulation of problems with movable geometry or boundary conditions. These methods also are strongly dependant on the reliance of a mesh.
Unlike finite element methods, mesh-free methods do not require a structured mesh; instead, only a scattered set of nodal points is required in the domain of interest. The objective of meshless methods is to eliminate the mesh-dependent structure of the classical mesh-based methods, by constructing the approximation entirely in terms of nodes.
The meshless methods have experienced a strong development in computational mechanics but most development has been focused on deterministic problems. Research in meshless methods that consider probabilistic analysis have not received much attention. Research in stochastic meshless methods for solving linear-elastic problems involving spatially varying random material properties have been presented in .
Among meshless methods, the EFG method is particularly appealing as a result of their simplicity and a formulation that corresponds to the well-established finite element method .
This paper presents a reliability procedure that couples first and second order reliability methods  and heuristic-based optimization method with an element-free Galerkin method. Rojas et al.  give more details of heuristic-based optimization method. Numerical applications in statics problems are used to illustrate the applicability and effectiveness of proposed methodology. These examples consist in a bar and a beam whose load, material and geometrical parameters are considered as random variables. The results show that the predicted reliability levels are accurate in comparison with similar approach that uses analytical and finite element analysis to evaluate the limit state functions. The results demonstrate the applicability, accuracy and efficiency of the proposed method.
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