A partition-of-unity based ‘FE-Meshfree’ QUAD4 element with radial-polynomial basis functions for static analyses

Recently, a partition-of-unity (PU) based finite element called ‘FE-Meshfree’ QUAD4 element has been published. That element employed polynomial basis functions for the local approximation (LA). In the present paper, a new FE-Meshfree QUAD4 element employing hybrid radial-polynomial basis functions for the LA is proposed. An advantage of radial-polynomial basis is the freedom from the possible singularity of the moment matrix that could sometimes result with an inappropriate choice of polynomial basis functions. Another advantage is the improved accuracy of finite element solution. The new element has been applied to several linear and nonlinear test problems. The results demonstrate that the new element gives much better performance as compared to the previous FE-Meshfree QUAD4 element with pure polynomial basis. Even with a lower order basis, viz., with just three or four polynomial terms, the present element is capable of giving more accurate solution than the previous element which employs a six-term polynomial basis. The new element also exhibits a much higher degree of tolerance to mesh distortion than the known quadratic elements. Moreover, the linear dependence problem, otherwise associated with many of the partition-of-unity (PU) based elements, is completely eliminated from the present element.