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摘要
This work presents a meshless numerical method for the solution of the linear elasticity equation, based on local collocation with radial basis functions and global reconstruction using an integral representational formula. Starting from a set of nodes distributed over the domain interior and boundaries, a small local stencil is formed around each interior node by connecting it to its neighbours. Over each local stencil a radial basis RBF) collocation is defined, which enforces the PDE governing and boundary operators. In this way the solution domain is covered by a series of small overlapping local RBF collocation systems. At each interior node the displacement field is approximated from the surrounding RBF collocation system and expressed in terms of its corresponding integral representational formula (Betti%26apos;s formula) defined over a local contour. In this way the approach can be considered to be an improved local Boundary Element method (LBEM) where besides using a direct interpolation of the displacement field, the PDE and boundary conditions are also imposed within the local interpolation. The resulting sparse global assembly is then solved to obtain the displacement field at each interior node. %26lt;br%26gt;Two benchmark problems with known analytical solutions are considered to test the performance of the method: a thin plate with a circular hole under traction, and a cylindrical annulus under internal and external pressure. Using these two numerical examples the accuracy of the proposed method is investigated, considering different configurations for the local integration contour, different quadrature schemes, the effect of basis function flatness, and spatial convergence rates. To allow a consistent analysis of these features regular nodal distributions are used for most investigations, however the capability of the method to operate on irregular datasets is also demonstrated.
- 出版日期2014-11
