有限覆盖径向点插值方法理论及其应用

数值流形方法能够统一地处理连续与非连续变形问题,有限覆盖技术是这种方法的核心。无网格方法前处理过程比较简单,径向点插值法是其中的一种计算格式。本文将有限覆盖技术与径向点插值方法相结合发展了有限覆盖径向点插值无网格方法,综合了数值流形方法与点插值方法的各自优点,能够有效地处理连续与非连续性问题,由此所构造的形函数具有Kronecker δ-函数属性,能够有效地处理位移边界条件。本文在阐述了这种方法基本原理的基础上,通过算例分析与数值计算论证了本文所建议方法的可靠性及其有效性。

The radial point-interpolation procedure based on finite covers and its applications

Numerical manifold method can solve both continuous and discontinuous deformation problems in a unified mathematical formulation. The finite cover is the essential technique in this method. The element-free methods have a relative simple pre-treatment process. The radial point-interpolation procedure is one of the element-free methods. In this paper, both the finite-cover technique and radial point- interpolation method are integrated together to develop a element-free radial point-interpolation procedure based on finite covers which takes both advantages of these two types of numerical methods. The shape functions constructed by the proposed method have the property of Kronecker d-function which made the essential boundary conditions be easily implemented. The fundamental theory of this procedure is illustrated and numerical analyses of examples show that the proposed procedure is an effective and simple method with higher computational accuracy.