Subdomain Techniques in EFGM for Parallel Processing
Ho Young Jo
Element-Free Galerkin Method (EFGM) is used mainly for crack analysis. But to get high accuracy of solutions, more degree-of-freedom (DOF) is needed. In this case more analyzing time is needed and analysis is restricted by computer memory. This paper presents subdomain techniques in EFGM. The method using Penalty function as a constraint and the method using Lagrange multiplier as a constraint are presented and the validities of these methods are demonstrated by a example.
To analyze high DOF problem, parallel processing is introduced with subdomain techniques. A domain is divided into several domains and each divided domain is taken by each CPU. In each CPU a stiffness matrix is constructed and matrix condensation is performed respectively. Final equation, which only interface DOF is in, is constructed and solved. The validity of this process is demonstrated by a example.
For the analysis of fatigue crack growth, the effects of the singularity of crack tip and the discontinuity of crack are considered by numerical techniques. To avoid discontinuities of the shape functions in crack tip fields, the dffraction method is used. J-integral is used to evaluate stress intensity factor and maximum circumferential stress theory is used to measure the direction of crack growth and Paris equation is used to measure the extension of fatigue crack growth. For the analysis of fatigue crack growth, much analyzing time is needed. To settle this problem, A coupled FEM-EFGM by a subdomain technique is proposed and the validity of this method is demonstrated by a example.
Element-Free Galerkin Method, subdomain techniques, parallel processing, fatigue crack growth, coupled FEM-EFGM