An Edge-Based Smoothed Point Interpolation Method for Material Discontinuity

摘要

In this work, the edge-based smoothed point interpolation method (ES-PIM) is extended to treat material discontinuity problems. The PIM shape functions used in the ES-PIM possess the Delta function property, which allows straightforward imposition of point essential boundary conditions and, hence, no additional treatment needs to be applied along the interface to meet the interface condition. By performing the generalized strain smoothing operation within the edge-based smoothing domains, the ES-PIM models possess a number of good features compared with the standard FEM using the same set of linear triangular elements, such as better accuracy, higher convergence rate, and efficiency. Three typical numerical examples, including the benchmark sandwiches cantilever beam, a hollow cylinder with two different materials and an automotive part of complicated shape, have been studied using the present ES-PIM. Analytical solutions for the first two problems have also been derived and presented. Very good agreement between the numerical results and the given analytical reference solutions demonstrate the effectiveness of the present ES-PIM method.