การปรับปรุงวิธีไฟไนต์พอยต์สำหรับปัญหากลศาสตร์ของแข็ง

Abstract

This thesis aims to study on mechanical problems via finite point method with additional term to improve accuracy of the solution. The stabilized parameter in additional term are categorized into 3 scenarios; zero parameter or no additional term, longest distance from star-point to surrounding point in the cloud, and nearest distance from star-point to surrounding point in the cloud. Experiment with one-dimensional and two-dimensional solid mechanics problems; uniform bar subjected to axial force, deep beam subjected to shearing stress at free-end, and trapezoidal beam subjected to axial stress; are considered. The accuracy of the displacements, strains and stresses are compared. The results shown that inaccurate solutions occurred for all cases when using the longest distance stabilized parameters. The case of no additional term provides fairly accurate result in two-dimensional deep beam subjected to shear stress at free-end. Lastly, using nearest distance from star-point to surrounding point as a stabilized parameter provides desirable results both in one-dimensional problem and trapezoidal beam subjected to axial stress problem.