A “FE-meshfree” QUAD4 element based on partition of unity

A new 4-node quadrilateral element is developed by combining the shape functions of finite element and meshfree methods. The objective is to synergise the attractive features of finite element and meshfree shape functions using the concepts of partition of unity (PU) methods. The shape functions of the well known QUAD4 element are used for PU and the least-square point interpolation for local approximation. This enables the proposed element inherit the compatibility properties of finite element method and the quadratic polynomial completeness properties of meshfree methods. Numerical results for the bench mark problems show that the proposed element has a good tolerance to distorted meshes. The element also seems to be free from the linear dependence problem which is known to plague some of the PU-based elements.