Development of meshfree methods for three-dimensional and adaptive analysis of solid mechanics problems

Abstract

This thesis focuses on the development and application of meshfree methods for computational mechanics. The first part of the thesis is to extend the meshfree radial point interpolation method (RPIM) for 3D problems. Effect of shape parameters is thoroughly investigated and some 3D numerical cases are studied. Results show that the RPIM has a very good performance for the analysis of 3D elastic problems. The second part is to develop a nodal integration scheme for the meshfree RPIM (NI-RPIM), in which the nodal integration scheme is stabilized by using Taylora??s expansion. The NI-RPIM can obtain very stable results and shows better performance compared with the linear FEM and the RPIM using Gauss integration. The third is to develop a linearly conforming point interpolation method (LC-PIM) for both 2D and 3D problems, and applied it in the adaptive analysis. The LC-PIM employs PIM shape function, a generalized Galerkin weak form is used to discretize the system equations and a stabilized nodal integration scheme with strain smoothing is used to perform the numerical integration. The LC-PIM possesses a number of properties including the upper bound property.