A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates

The meshfree approximation functions for shell analysis to date are formulated using parametric coordinates, and this parametric description of shell kinematics limits the applications only to shell structures with simple geometries. On the other hand, construction of moving least square or reproducing kernel (RK) approximation on shell surface using Cartesian coordinates leads to a singular system when RK basis functions and shell surface function are linearly dependent. In this study, a constrained RK approximation formulated under Cartesian coordinate for approximation of shell kinematics in arbitrary shell geometry is proposed. Two methods, the dummy node approach and the pseudo-inverse method, are presented. Further, stabilization of nodal integration for solving shear deformable shell is introduced. The performance of present formulation is demonstrated in several benchmark problems. Copyright 2006 John Wiley & Sons, Ltd