Research on computational approaches using element-free Galerkin methods

Element free Galerkin method (EFGM) is a new computational method for solving partial differential equation, in which there is no need to generate FE elements and only the information of nodes not the connective information is needed. This work is mainly concerned with four problems, such as constructing moving least square (MLS) approximation to construct the shape function, developing control equation with the weak variational form, enforcing the essential boundary condition and integrating the design domain using Gauss method, where the shape function derived from MLS method generally canpsilat meet Kronecker condition around the essential boundary and it can be settled by employing Lagrange multiplies. A typical example is performed to substantiate the validity of EFGM accompanied with the comparison of analytical result and FE approximation.