More importantly, the RKs taken here are used not only for the interpolation of the curved geometry, but also for the approximation of field variables. A convected coordinate system is introduced into the formulation to deal with the curvilinear surface. The stiffness matrix is derived using the stabilized conforming nodal integration technique. A singular kernel is introduced to impose the essential boundary conditions because of the RK shape functions, which do not automatically possess the Kronecker delta property. In this setting, the meshfree interpolation functions are derived from the RK. There are five degrees of freedom per node (i.e., three displacements and two rotations). The present meshfree curvilinear shell model is based on Reissner-Mindlin plate formulation, which allows the transverse shear deformation of the curved shells. A Galerkin meshfree reproducing kernel (RK) approach is then developed. In particular, shallow shell, cylinder and perforated cylinder buckling problems are considered. The paper is concerned with eigen buckling analysis of curvilinear shells with and without cutouts by an effective meshfree method.
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