In the present work, a novel hybrid FE-Meshless quadrilateral element with continuous nodal stress is developed using radial-polynomial basis functions, named as Quad4-RPIMcns. Quad4-RPIMcns can be regarded as the development of the previous FE-Meshless quadrilateral element with radial-polynomial basis functions (Quad4-RPIM) and quadrilateral element with continuous nodal stress (Quad4-CNS). Similar to Quad4-RPIM, radial-polynomial basis functions are used to construct nodal approximations of Quad4-RPIMcns in the context of partition of unity, which avoids the possible singularity problem of constructing nodal approximations. The derivative of Quad4-RPIMcns shape function is continuous at nodes. Therefore, nodal stress can be obtained without any extra operation. Quad4-RPIMcns possesses Kronecker-delta property which is a very important property to impose essential boundary conditions directly as in the FEM. The numerical tests in this paper demonstrate that Quad4-RPIMcns gives better accuracy and higher convergence rate as compared to four-node iso-parametric quadrilateral element (Quad4). Additionally, Quad4-RPIMcns seems to have higher tolerance to mesh distortion than Quad4. 
A hybrid ‘FE-Meshless’ QUAD4 with continuous nodal stress using radial-polynomial basis functions