The present study is concerned with an application of the global local finite element method (GLFEM) to a gear tooth stress analysis. The GLFEM is a numerical analysis technique which combines finite element solutions and classical analytical ones on the basis of the energy principle. In this method, the classical analytical solutions give an almost exact stress field to the elements in which the stress varies very rapidly and/or the stress concentration is found. A fine subdivision, therefore, is not required. In the application of the conventional finite element method to the gear tooth stress analysis, the fine subdivision is required especially at the positions near tooth bottom and the load applied point. Hence, only two-dimensional analysis is available for common use. Furthermore, in order to determine an exact location of a critical section on which a fillet stress is maximum, we must use complicated procedures, e.g., an iteration of subdivision for searching the maximum nodal stress. In the present paper, the GLFEM is applied to the gear tooth stress analysis to show that even the rough subdivision enables us to make the precise three-dimensional analysis. It also guarantees an easy determination of the critical section. Thus, we show the effective future of the GLFEM to the gear tooth stress analysis.
Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure
