Stress Analysis of Linear Elastic Solid Problems by using Enhanced Meshfree Method based on Fast Derivatives Approximation

고속 도함수 근사화에 의해 개선된 무요소법을 이용한 선형탄성 고체문제의 응력해석

Point collocation method based on the fast derivatives approximation of meshfree shape function is applied to solid mechanics in this study. Enhanced meshfree approximation with approximated derivative of shape function is reviewed, and formulation of linear elastic solid mechanics by point collocation method is presented. It implies that governing equation of solid mechanics with strong form is directly formulated without no numerical integration cells or grid. The regularity of weight function is not required due to a use of approximated derivative, so we propose the exponential type weight function that is discontinuous in first derivative. The convergence and stability of the proposed method is verified by passing the generalized patch test. Also, the efficiency and applicability of the proposed method in solid mechanics is verified by solving types of solid problems. Numerical results show that not only a use of proposed weight function leads lower error and higher convergence rate than that of the conventional weight functions, but also the improved collocation method with derivative approximation enables to compute the derivatives of shape function very fast and accurately enough to replace the classical direct derivative calculation.