Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads

Abstract

SUMMARYIn this paper, a mesh-free approach is employed for buckling analysis of Mindlin plates that are subjected to in-plane point loads. The radial point interpolation method (RPIM) is used to approximate displacements based on nodes. Variational forms of the system equations are established. Two-step solution procedures are implemented. The non-uniform pre-stress distribution of plate is first obtained using the RPIM based on a two-dimensional (2D) elastic plane stress problem. This predetermined non-uniform pre-stress distribution is then used to compute buckling loads of plate using the RPIM based on Mindlin's plate assumption. The RPIM can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads. Numerical examples considered here include circular and rectangular Mindlin plates that are subjected to in-plane uniform and point loads with different aspect ratios and boundary conditions. The present results are validated against the available analytical and numerical solutions.

A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems

“…The square definition domain with edge length 2.0h was used in the original RPI approximation given by Wang et al [11,13], where h was the maximum distance among neighbouring nodes. In Liew and Chen [29,30] work, the size of the quadrilateral definition domain was taken as three times of the average nodal distance.…”

“…Hon et al further extended the method to solve various non-linear initial plate. Liew and Chen [29,30] solved the buckling problems of Mindlin plates with the RPI method.…”

Multiscale simulation of nanostructures based on spatial secant model: a discrete hyperelastic approach

“…In this context, we have developed a meshfree approach in order to capture the non-linear responses of shell-like structures in CNT. For general reviews on the meshfree and particle methods and application to shell and plate structures, we refer to the work described in [15][16][17][18][19][20][21][22][23][24][25][26]. Comparing with the standard continuum treatment of shell or plate, an important difference in the developed meshfree approach in this paper is the fact that the "thickness" of the single layer of CNT is considered to be zero.…”

Analyzing three-dimensional potential problems with the improved element-free Galerkin method

“…There are several meshless methods: the diffuse element method [2], the element-free Galerkin (EFG) method [3], the Hp clouds method [4], the harmonic reproducing kernel particle method [5], the meshless local Petrov-Galerkin method [6], the multi-scale reproducing kernel particle method [7][8][9], the wavelet particle method [10], the radial point interpolation method [11][12][13], the complex variable meshless method [14], the boundary element-free method [15][16][17][18], the moving least-squares differential quadrature meshfree method [19,20]. The common feature of these methods, of which the EFG method is the most widely applied, is that they do not use predefined meshes, at least for field variable interpolation.…”