$meshfree particle methods for thin plates$

The foundation of the present development is the construction of smoothed meshfree gradients with linear basis function, where the second order smoothed gradients are expressed as combinations of standard first order gradients and the computational burden is remarkably reduced. In this work, a gradient smoothing Galerkin meshfree method with particular reference to the linear basis function is proposed for thin plate analysis. However, due to the rational nature of reproducing kernel meshfree shape functions, the computation of the second order derivatives of meshfree shape functions is quite complex and costly, which also requires expensive high order Gauss quadrature rules to properly integrate the stiffness matrix.

Thus at least a quadratic basis function should be utilized in meshfree approximation to enable the Galerkin meshfree thin plate analysis. The fourth order governing equation of thin plate necessitates the employment of C$^$ continuous shape functions with a minimum degree of two in a Galerkin formulation.

Meshfree particle methods for thin plates