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Keywords: meshless methods, gradient-based methods reliability, heuristic based reliability method.

Summary

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 [1].

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 [2].

This paper presents a reliability procedure that couples first and second order reliability methods [3] and heuristic-based optimization method with an element-free Galerkin method. Rojas et al. [4] 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.

References

1: B.N. Rao, S. Rahman, "Probabilistic Fracture Mechanics by Galerkin Meshless Methods - Part I: Rates of Stress Intensity Factors", Computational Mechanics 28, 351-364, 2002. doi:10.1007/s00466-002-0299-x
2: Y.Y. Lu, T. Belytschko, L. Gu, "A New Implementation of the Element-free Galerkin Method", Computer Methods in Applied Mechanics and Engineering 113, 397-414, 1994. doi:10.1016/0045-7825(94)90056-6
3: A. Der Kiureghian, M. De Stefano, "Efficient algorithm for second-order reliability analysis", Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 117, 12, 1991. doi:10.1061/(ASCE)0733-9399(1991)117:12(2904)
4: J.E. Rojas, F.A.C. Viana, D. Rade, V. Steffen Jr., "A Procedure for Structural Reliability Analysis Based on Finite Element Modeling", IV Congresso Nacional de Engenharia Mecânica, 22 a 25 de Agosto 2006, Recife-PE, Brasil, 2006.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 86 PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping Paper 41 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 ²School of Mechanical Engineering, Federal University of Uberlândia, Brazil doi:10.4203/ccp.86.41 purchase the full-text of this paper Full Bibliographic Reference for this paper 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. Summary 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 [1]. 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 [2]. This paper presents a reliability procedure that couples first and second order reliability methods [3] and heuristic-based optimization method with an element-free Galerkin method. Rojas et al. [4] 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. References 1 B.N. Rao, S. Rahman, "Probabilistic Fracture Mechanics by Galerkin Meshless Methods - Part I: Rates of Stress Intensity Factors", Computational Mechanics 28, 351-364, 2002. doi:10.1007/s00466-002-0299-x 2 Y.Y. Lu, T. Belytschko, L. Gu, "A New Implementation of the Element-free Galerkin Method", Computer Methods in Applied Mechanics and Engineering 113, 397-414, 1994. doi:10.1016/0045-7825(94)90056-6 3 A. Der Kiureghian, M. De Stefano, "Efficient algorithm for second-order reliability analysis", Journal of the Engineering Mechanics Division, American Society of Civil Engineers, 117, 12, 1991. doi:10.1061/(ASCE)0733-9399(1991)117:12(2904) 4 J.E. Rojas, F.A.C. Viana, D. Rade, V. Steffen Jr., "A Procedure for Structural Reliability Analysis Based on Finite Element Modeling", IV Congresso Nacional de Engenharia Mecânica, 22 a 25 de Agosto 2006, Recife-PE, Brasil, 2006. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £120 +P&P)
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