Meshfree point collocation method for elasticity and crack problems

A generalized diffuse derivative approximation is combined with a point collocation scheme for solid mechanics problems. The derivatives are obtained from a local approximation so their evaluation is computationally very efficient. This meshfree point collocation method has other advantages: it does not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. The accuracy of the solutions is exceptional and generally exceeds that of element-free Galerkin method with linear basis. The performance and robustness are demonstrated by several numerical examples, including crack problems.