ABSTRACT
With the wide engineering applications of plate structures with complex geometry, static and dynamic analyses of plates with complicated shapes become very important. However, exact analyses of such plates are usually very difficult. Therefore, numerical techniques with different discretization schemes such as the finite element method (FEM) have been developed. FEM has achieved remarkable success in static and dynamic analyses of plates. Meshfree methods have also been developed for analysis of plates. Krysl and Belytschko
[1,2] have extended the element-free Galerkin (EFG) method to static analysis of thin plates and shells. In their work, the essential boundary conditions are enforced by a method of Lagrange multipliers. An EFG method has also been formulated for modal analyses of Euler-Bernoulli beams and Kirchhoff plates [3]. EFG has also been formulated for dynamic problems [4], buckling problems of thin plates [5,6], as well as composite laminates [5-7]. In these works, the essential boundary conditions are imposed using orthogonal transform techniques. EFG formulations for thick plates were presented for both static and dynamic problems
based on the first-and third-order shear deformation theories [4]. When using higher-order plate theories, the well-known issue of shear locking arises. Therefore, different methods for eliminating shear locking have also been discussed. Point interpolation methods (PIMs) based on weakened-weak (W2) formulations and
PIM shape functions with the Kronecker delta function property have also been formulated for plates. The work is still in progress, and some of the current works on edge-based smoothed point interpolation method (ES-PIM) that are very stable and efficient will be presented in this chapter. This chapter is dedicated to meshfree methods for analysis of plates. Both formulations
and applications of EFG and PIMs will be presented in detail. Problems considered include static deformation, buckling, and dynamic response of thin and thick plates, including composite laminated plates.
