Lower bound shakedown analysis by the symmetric Galerkin boundary element method |
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| Institution: | 1. School of Mechanics & Civil Engineering, China University of Mining and Technology, Beijing 100083, China;2. State Key Laboratory for Geomechanics and Deep Underground Engineering, Beijing 100083, China;3. Department of Civil, Environmental and Geo-Engineering, University of Minnesota, United States;1. Department of Engineering Mechanics, AML, Tsinghua University, Beijing 100084, China;2. Institute of Electronics Packaging Technology and Reliability, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China;1. Department of Civil Engineering, International University - VNU HCMC, Viet Nam;2. Faculty of Civil Engineering, HCMC University of Technology and Education, Viet Nam |
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| Abstract: | In this paper, the static shakedown theorem is reformulated making use of the symmetric Galerkin boundary element method (SGBEM) rather than of finite element method. Based on the classical Melan’s theorem, a numerical solution procedure is presented for shakedown analysis of structures made of elastic-perfectly plastic material. The self-equilibrium stress field is constructed by linear combination of several basis self-equilibrium stress fields with parameters to be determined. These basis self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains obtained through elastic–plastic incremental analysis. The lower bound of shakedown load is obtained via a non-linear mathematical programming problem solved by the Complex method. Numerical examples show that it is feasible and efficient to solve the problems of shakedown analysis by using the SGBEM. |
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