Mechanical Engineering Journal (Aug 2016)
An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
Abstract
In s-version finite element method (s-FEM) proposed by Fish (1992), a local mesh that represents the local feature such as a hole or a crack is superposed on a global mesh that represents the shape of the whole analysis model. The interaction between global and local meshes is represented by coupling stiffness matrices. Since the global and local meshes can be generated independently, mesh generation efforts are reduced remarkably. However, s-FEM has a common issue. The generation of coupling stiffness matrices takes a considerable amount of program development efforts, which include constructing accurate cross-element integration methodology and programming it for various element types. For such an issue, we propose an iterative s-FEM that does not require the generation of coupling stiffness matrices at all. The coupling term is now evaluated by global and local stresses that are computed on the respective mesh and then transferred to the other by interpolation techniques. The global and local stresses are treated as initial stress in the finite element computations. The global and local analyses are performed alternately under assumed initial stress, and converged solution is achieved by iteration with a monitored residual being sufficiently small. In proposed iterative s-FEM, an issue about linear independence of global and local elements, which is known to occur in the original s-FEM, does not occur. In numerical experiments, converged solution was successfully obtained within several hundred iteration counts. Accurate stress distribution for a stress concentration problem and an accurate stress intensity factor for a linear elastic fracture mechanics problem were computed by proposed iterative s-FEM. In addition, several stress interpolation techniques were compared in the numerical experiments. Nearest neighbor interpolation for the global stress and local least squares interpolation for the local stress showed good convergence and accurate solution.
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