A point assembly method for stress analysis for two-dimensional solids |
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| Affiliation: | 1. Mathematical center for interdisciplinary research and School of Mathematical Sciences, Soochow University, Suzhou, 215006, China;2. Mathematics Department, South Hall 6705, University of California, Santa Barbara, CA 93106, USA;3. BCAM – Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Basque Country, Spain;1. Campus Saint-Jean and Mathematical Department, University of Alberta, Edmonton, Canada;2. Department of Mathematics and Statistics, Laval University, Québec, Canada;3. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada;1. Graduate Program in Mechanical Engineering, Pontifical Catholic University of Paranã, Rua Imaculada Conceição, 1155, CEP: 80.215-901, Curitiba, PR, Brazil;2. Graduate Program in Numerical Methods in Engineering, Federal University of Paranã, Centro Politécnico, Bloco Lame/Cesec Caixa Posta 19011, CEP: 81531-990, Curitiba, PR, Brazil;3. Graduate Program in Civil Engineering, Federal Technological University of Paranã, Rua Dep. Heitor Alencar Furtado, 4900, CEP: 81.280-340, Curitiba, PR, Brazil;1. Aerospace and Ocean Engineering Department, Virginia Tech, Blacksburg, VA 24061, USA;2. Math Department, Virginia Tech, Blacksburg, VA 24061, USA |
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| Abstract: | A novel point assembly method (PAM) is presented for stress analysis for two-dimensional solids. In the present method, the boundaries of the problem domain are represented by a set of discrete points, and the domain itself is represented by properly scattered points. The displacement in the influence triangular areas of a point is interpolated by the displacements at the point and pairs of surrounding points using shape functions. The shape functions used in this work are obtained in the same way as those of a triangular element in the conventional finite element method (FEM). A variational (weak) form of the equilibrium equation is used to produce a set of system equations. These equations are assembled for all the points in the domain, and solved for the displacement field. Stresses and strains at a point are then computed using the displacements obtained for the point and pairs of the surrounding points. A PAM program with an automatic point-searching algorithm has been developed in fortran. Patch tests and convergence studies have been carried out to verify the convergence of the present method and program. Examples are also presented to demonstrate the efficiency and accuracy of the present method compared with analytical solutions as well as the conventional FEM solutions. |
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