Application of the 'FE-Meshfree' QUAD4 with continuous nodal stress using radial-polynomial basis functions for vibration and geometric nonlinear analyses

A hybrid 'FE-Meshfree' four-node quadrilateral element with continuous nodal stress using radial-polynomial basis functions (Quad4-RPIMcns), was recently proposed for static analysis. The Quad4-RPIMcns element can be considered as a development of the previous partition-of-unity (PU) based 'FE-Meshfree' QUAD4 element (Quad4-RPIM) which uses FE shape functions to construct the PU and radial-polynomial basis functions to construct the local approximation (LA), so as to synergize the individual strengths of finite element and meshfree methods. As a result, high order global approximations in Quad4-RPIMcns element could be easily constructed without adding extra nodes and DOFs, thereby achieving high accuracy and convergence rate. In this paper, the element is further applied to conduct free vibration, forced vibration and geometric nonlinear analyses of two-dimensional solids. Several numerical test problems are solved and the performance of the element is compared with that of the three-node triangular element (Trig3) and four-node isoparametric quadrilateral element (Quad4). Numerical results show that Quad4-RPIMcns element has higher tolerance to mesh distortion and gives more accurate solution as compared to Trig3 and Quad4 elements.