The meshless methods are the newly developed approximation method that estimates the solution of differential equation by nodal configuration only. Especially, this method is suitable for adaptive analysis and crack analysis, since it is possible to easily construct the new analysis model by only adding some nodes. In this thesis, the adaptive schemes that can maximize the merit of meshless method are studied by Element-free Gelerkin method that is one of the meshless methods.
The error estimation, the first step of adaptive analysis is performed by the stress projection method. This method is based on the property of meshless method that the spurious oscillations of stress are occurred in high stress gradient area. The major procedures of the stress projection are the projection of nodal stress by another EFG shape function that have smaller influence domain than that of original EFG analysis. The obtained stress profiles by the stress projection method are used as reference solution. These schemes are verified by several 1-dimensional and 2-dimensional numerical examples.
To perform adaptive analysis as obtained approximation error, two types of refinement scheme, the cell-dividing scheme and the triangulation scheme, are newly proposed. Both proposed schemes show the efficiency of analysis and the good convergence behaviors. In viewpoint of convergence, the cell-dividing scheme shows better performance. And the triangulation scheme that integration cells are constructed by Delaunay triangulation shows the more “mesh-free” behaviors. The main advantages of proposed schemes are the efficiency of analysis model in crack propagation analysis, since the optimum models of analysis are constructed every propagation step by the refinement and recovery.
To evaluate the performance of proposed adaptive procedure, several 2-dimensional examples including crack propagation problems are investigated. The obtained response by the adaptive analyses including crack propagation analysis, such as convergence ratio, stress intensity factor and propagation path, show the validity and efficiency of proposed adaptive scheme. As a further study, the better error estimation scheme to obtain more smooth error profile and the new nodal arrange scheme that are independent from integration cell are presented. Additional, to ensure the validity in practical problem, the study for fatigue analysis and the various case studies are required.