Development of meshfree methods for plates

Abstract

A meshfree method, element free Galerkin (EFG) method, approximates displacements based on a set of scattered nodes. The moving least squares (MLS) technique in the EFG method may easily produce high-order approximated displacement fields. The EFG method has rapid convergence, high accuracy and good stability. This thesis develops the EFG method for the analyses of static bending, free vibration and static buckling of thin plates, symmetrically laminated composite plates and shear deformable plates based on the classical, first- and third-order shear deformable plate theories. To impose essential boundary conditions, penalty method for bending analyses, and a weak form with Lagrange multipliers and orthogonal transformation technique for eigenvalue analyses are used. A radial point interpolation method (RPIM) is also developed for static bending and buckling analyses of shear deformable plates. The RPIM shape functions possess delta function properties. Numerical examples are presented to demonstrate the effecitivenes of these methods.