Meshless methods for shear-deformable beams and plates Original Research Article

A meshless method is developed to analyze moderately thick and thin structures using Mindlin-Reissner theory. A uniform discretization is used to allow for efficient integration and for the shape functions to be written explicitly. Irregular boundaries are modeled in a straightforward manner. An unmodified displacement-based Galerkin method is used; full integration is used to evaluate all energy terms and convergence is independent of the thickness. Shear and membrane locking are completely eliminated pointwise at the interpolant level using cardinal splines. The continuity of the splines chosen results in continuous stresses. An extension to general meshless methods is given. Beam and plate examples show the accuracy of this method for coarse discretizations