A ‘FE-Meshfree’ TRIA3 element based on partition of unity for linear and geometry nonlinear analyses

Abstract

A new 3-node triangular element is developed on the basis of partition of unity (PU) concept. The formulation employs the parametric shape functions of classical triangular element (TRIA3) to construct the PU and the least square point interpolation method to construct the local displacement approximation. The proposed element synergizes the individual merits of finite element method and meshfree method. Moreover, the usual linear dependence problem associated with PU finite elements is eliminated in the present element. Application of the element to several linear and geometric nonlinear problems shows that the proposed element gives a performance better than that of classical linear triangular as well as linear quadrilateral elements, and comparable to that of quadratic quadrilateral element. The proposed element does not necessitate a new mesh or additional nodes in the mesh. It uses the same mesh as the classical TRIA3 element and is able to give more accurate solution than the TRIA3 element.