탄성균열해석을 위한 그리드 없는 유한차분법 = A Gridless Finite Difference Method for Elastic Crack Analysis

다국어 초록 (Multilingual Abstract)

This study presents a new gridless finite difference method for solving elastic crack problems. The method constructs the Taylor expansion based on the MLS(Moving Least Squares) method and effectively calculates the approximation and its derivatives without differentiation process. Since no connectivity between nodes is required, the modeling of discontinuity embedded in the domain is very convenient and discontinuity effect due to crack is naturally implemented in the construction of difference equations. Direct discretization of the governing partial differential equations makes solution process faster than other numerical schemes using numerical integration. Numerical results for mode I and II crack problems demonstrates that the proposed method accurately and efficiently evaluates the stress intensity factors.

참고문헌 (Reference)

1 "무요소법의 약정식화와 강정식화를 위한 일관된 분산미분근사 (2): 수치예제 중심으로" 25 (25): 915-922, 2005b

2 "무요소법의 약정식화와 강정식화를 위한 일관된 분산미분근사 (1) : 수학적 이론배경 및 이산화" 25 (25): 907-913, 2005a

3 "Theory of Elasticity" 1970

4 "The stress analysis of cracks handbook" 1973

5 "The immersed interface method for elliptic equations with discontinuous coefficients and singular sources" 1994

6 "The Immersed Interface Method for the NavierStokes Equations with Singular Forces" 171 : 822-842, 2001

7 "Stability and instability in the computation of flows with moving immersed boundaries a comparison of three methods" 1992

8 "Point collocation methods using the fast moving least square reproducing kernel approximation" 56 : 1445-1464, 2003

9 "Meshfree point collocation method for elasticity and crack problem" 61 : 22-48, 2004

10 "International Journal for Numerical Methods in Engineering" -256, 1994

11 "Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain" 191 : 106-125, 2006

12 "Crack tip and associated domain integrals from momentum and energy balance" 1987

13 "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity Journal of Applied Mechanics" 1980

14 "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity Journal of Applied Mechanics" 1980

15 "A generalized finite-difference method based on minimizing global residual" 191 : 1421-1438, 2002

16 "A finite point method for elasticity problems" 79 : 2151-2163, 2001

17 "A fast iterative algorithm for elliptic interface problems" 35 : 230-254, 1998