EIGENVALUE ANALYSIS OF THIN PLATE WITH COMPLICATED SHAPES BY A NOVEL MESH-FREE METHOD

Abstract

Further development of a novel mesh-free method for eigenvalue analysis of thin plate structures with complicated shapes is presented in this paper. A mesh-free method used the moving Kriging interpolation technique for constructing the shape functions, which possess the Kronecker's delta property, is formulated. Thus, it makes the present method efficient in enforcing the essential boundary conditions and none of any special techniques are required. The present plate theory followed the classical Kirchhoff's assumption and the deflection is in general approximated through the moving Kriging interpolation. Also, the mesh-free formulations for the vibration problem are formed in a simple way as finite element methods. The orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. A standard weak form is adopted to discrete the governing partial differential equation of plates. Some numerical examples are attempted to demonstrate the applicability, the effectiveness, and the accuracy of the method.