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Structural Engineering and Mechanics
  Volume 15, Number 5, May 2003, pages 535-550

A boundary radial point interpolation method (BRPIM) for 2-D structural analyses
Y. T. Gu and G. R. Liu

    In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.
Key Words
    meshless method; meshfree method; boundary integral equation; boundary element method; radial basis function; numerical analysis.
Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

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