Nonlinear meshfree formulation of nonlinear geometric composite beam with slip

Abstract

Meshfree (MFree) method is one of the latest numerical techniques after the established Finite Element Method (FEM), Finite Difference Method (FDM) and Boundary Element Method (BEM). Therefore, MFree method is still in its early development stage where many practical engineering problems are still had not been considered. Accordingly, this study focuses on the formulation of MFree solution for nonlinear geometric composite beam with slip by using the Multi Quadrics Radial Basis Function (MQ-RBF) of Radial Point Interpolation Method (RPIM). For verification purposes, Finite Element (FE) solution has also been formulated for the same problem to act as the benchmark model. Comparison of result between MFree and FEM has revealed that, whilst there is insignificant difference in terms of the convergence rate, FEM performs better in terms of computer resources. Parametric study has been conducted in determining the effects of various MFree variables to the performance of the MFree solution. These variables are the size of support domain, the number of gauss point, the number of bending and axial nodes, the dimensionless shape parameters caand q as well as the number of polynomial basis, m. It has been found that the size of support domain is the most influential variable in governing the convergence rate of the formulation. From the study, it can be concluded that MFree method of analysis has the potential to be the alternative numerical method in solving structural engineering problem especially for composite structures. However, further studies are required in improving the efficiency of the method specifically in regards to the high consumption of computer resources