Meshless method of radial point interpolation functions for elasticity Hamilton canonical equation

Meshless formulistic of Hamilton canonical equation was derived by combining the modified Hellinger-Reissner variational principle for elastic material and the radial point interpolation functions in this paper. Based on the shape functions of Multiquadric (MQ), Gaussian (EXP) and thin plane spine (TPS), the maximum displacements in z direction of the single laminated plates were obtained by the meshless formulistic of Hamilton canonical equation. All of the numerical results were compared with those of ANSYS, demonstrating that the meshless formulistic of Hamilton canonical equation is reliable. As an application of the present method, the convergence of this meshless formulistic and the effects of the dimensionless shape parameters on the maximum displacement were investigated through numerical examples of single laminated plates clamp supported on four sides. This study introduced the advantages of meshless finite element method into semi-analytic solution of Hamilton canonical equation, and a new semi-analytic method was presented for Hamilton canonical equation.