Meshfree formulation of geometric composite beam with partial interaction

Abstract

This study concerns with the formulation of Meshfree (MFree) for nonlinear geometric of composite beam with partial interaction. The Principle of Virtual Work was used to derive the differential equation of composite beam. Finite Element Method (FEM) and MFree method: Point Interpolation Method (PIM) was used to solve the differential equation. The derived formulation was validated with previous research work for linear problem and nonlinear problem. The nonlinear geometrical are taken into account to study the performance of Mfree handling the nonlinear problem and the performances are compared with FEM. The algorithms of the solution procedure for both methods were written in MATLAB. Parametric studies were conducted to study the performances in term of convergence rate and computer resources between FEM and PIM. The parameters considered in this study were the size of support domain, as number of nodes, number of Gauss cell and number of Gauss point. The result of the parametric study showed that five bending nodes and nine axial nodes with as equal to four give the appropriate result considering both accuracy and stability. The recommended value for Gauss cell was three and the number of Gauss point was five. Two parameters observed to study the use of computer resources were the computational speed and memory used to solved the problem. From the study, MFree has been found to have a potential as FEM yet another option of numerical method in solving engineering problem in general and composite beam problem in particular. However, further studies are required in improving the efficiency of the method specifically in regards to the high consumption of computer resources.