Dual reciprocity boundary element method using compactly supported radial basis functions for 3D linear elasticity with
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Dual reciprocity boundary element method using compactly supported radial basis functions for 3D linear elasticity with body forces Cheuk-Yu Lee . Hui Wang . Qing-Hua Qin
Received: 29 June 2015 / Accepted: 13 October 2015 Springer Science+Business Media Dordrecht 2015
Abstract A new computational model by integrating the boundary element method and the compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the supported radius in the CSRBF are obtained for inhomogeneous term interpolation. Subsequently, the classical dual reciprocity boundary element method, in which the domain integrals due to the presence of body forces are transferred into equivalent boundary integrals, is formulated by introducing locally supported displacement and stress particular solution kernels for solving the inhomogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present method.
Dr. Wang is currently visiting at ANU. C.-Y. Lee H. Wang Q.-H. Qin (&) Research School of Engineering, Australian National University, Acton, ACT 2601, Australia e-mail: [email protected] C.-Y. Lee e-mail: [email protected] H. Wang e-mail: [email protected] H. Wang Department of Engineering Mechanics, Henan University of Technology, Zhengzhou 450001, China
Keywords Three-dimensional linear elasticity Dual reciprocity method Boundary element method Compactly supported radial basis functions
1 Introduction It is noted that for 3D linear elasticity with the presence of arbitrary body forces, analytical solutions are available only for a few problems with very simple geometries, boundary conditions and body force terms such as gravitational forces (Piltner 1987; Wang and Zheng 1995; Qin and Mai 1997; Qin 2000; Qin and Ye 2004; Barber 2006; Lee et al. 2008). In most cases, as irregular geometries or boundaries are involved, numerical solutions are usually sought. Numerical methods such as the finite element method (FEM), the finite difference method (FDM) and the boundary element/integral method (BEM/BIM) provide alternative approaches to approximate the 3D elasticity solutions in the past decades (Jirousek et al. 1995; Qin and Mai 2002; Qin 2003, 2005; Bathe 2006). Among them, the FEM and the FDM require domain discretization while the BEM/BIM requires only boundary discretisation for the homogeneous partial differential equations (PDE) and thus has advantage of dimension reduction over the FEM/FDM. However, domain discretisation is generally unavoidable in the BEM/BIE for the inhomogeneous PDE problems like the 3D linear elasticity problems with arbitrary body forces under consideration. To make the BEM a truly
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boundary discretisation method for the inhomogeneous cases, a variety of domain transformation methods such as the radial integration method (RIM; Gao 2002) and the dual
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