Meshfree formulation of buckling of composite beam with slip

Abstract

This study concerns with the formulation of Meshfree methods for the buckling analysis of partial interaction of composite beam. Meshfree formulations of Polynomial Interpolation Method (PIM) and Radial Polynomial Interpolation Method (RPIM) have been developed where multi-quadric radial basis functions have been used as the interpolation functions. Comparison of the results for the buckling problem against analytical and existing numerical works showed good agreement thus validates the formulation. Parametric studies have been conducted to study the effect of the method’s parameters to the solution accuracy. The effects of support domain and gauss cell were extensively studied for the PIM method. For the RPIM method, parameters used for the parametric study were the support domain, gauss cell, and shape parameter. Once the optimum values of the parameters were obtained, convergence study was carried out to determine the rate of convergence of the Meshfree. It was found that the use of gauss cell proportional to the number of point gives the best convergence rate for the solution of the buckling load. Parametric studies for the analysis of composite beam interaction and geometric ratio have been also conducted for both finite element and Meshfree methods. It was be observed that partial interaction between top and bottom section occurs for some specific connector stiffness values. The effect of geometric ratio, on the other hand, showed that the partial interaction regime for the composite beam reduced as the geometric ratio increased. For all the parametric study conducted, result obtained from PIM and RPIM showed good agreement with converged finite element solution thus indicating the suitability of the Meshfree methods in the study of buckling analysis of composite beam with partial interactions.