An element free Galerkin Method for the prediction of soft tissue deformation in surgical simulation

Meshless methods based on Element Free Galerkin formulation exhibit three major limitations : a) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes; b) challenges in imposing the Essential Boundary Conditions (EBC), and, c) inaccurate numerical integration in space. To find effective solutions for the problems mentioned, the thesis presents a Modified Moving Least Squares method for interpolating scattered data, a novel way of imposing EBC for explicit meshless, and implements an adaptive numerical integration procedure. The effectiveness of the proposed methods is demonstrated using 2D and 3D numerical examples of soft tissue deformation.