Application of Transition Finite Elements in hpq-Adaptive Modeling and Analysis of Machine Elements

Abstract

This paper concerns modeling and analysis of machine elements using the adaptive finite element method. The adaptation used is of hpq type, which means that the finite element dimension h and element transverse q and longitudinal p approximation order may be different in each element. These parameters are determined automatically by the program so as to obtain modelling and approximation error levels not higher than the assumed admissible level of the errors. The presented paper focuses on the use of transition elements between basic elements corresponding to the three-dimensional theory of elasticity and the first-order shell model. Three applied transition elements differ in their assumptions regarding the continuity of the displacement, strain and stress fields between the basic models. The effectiveness of the application of transition elements was assessed in terms of: removal of the internal boundary layer at the boundary between the models and convergence of adaptive solutions taking into account these models.