A HERMITE INTERPOLATION ELEMENT-FREE GALERKIN METHOD FOR ELASTICITY PROBLEMS

We propose a Hermite interpolation element-free Galerkin method (HIEFGM) for elasticity problems by combining the Hermite approximation approach and an improved interpolation element-free Galerkin method (IIEFGM). The approximation function of the field quantity is constructed based on the moving least-squares method and the Hermite approximation approach. Employing the constitutive equation, geometric equation and Galerkin integral weak form, the discretization equation of the HIEFGM of elasticity problems is established. The proposed method considers the normal derivative of the displacements of boundary nodes in function approximation, so the accuracy of the IIEFGM is improved without increasing the number of nodes. Furthermore, the shape function has the property of a Kronecker delta function, which avoids the problems in dealing with the essential boundary condition. In numerical examples, the effects of the weight function, scaling factor, node density and node arrangement in accuracy and stability of the HIEFGM are discussed and the applicability of the HIEFGM is evaluated through comparing the present results with those of other available methods. The results suggest that the HIEFGM can effectively solve various elasticity problems with excellent accuracy and stability.