Application of the Cell Method in Elasticity Problems

Aim of this work is to show an application of Cell Method to the numerical elastic stress analysis of a lug and the consequent determination of stress concentrations on the contour of the hole, for the specified geometrical proportions and loading condition. In fact, although the investigated geometry has been widely studied in the past, and is used to model a variety of mechanical connections, still results found in literature do not always agree. The same elasticity problem in 3D has been also considered. Cell Method is a numerical method that has been recently introduced, and one of its main features is that it is particularly suitable to investigate stress concentration factors, as the error will not increase when decreasing the mesh size. Another feature of Cell Method is that solution with parabolic interpolation of displacement field is directly obtained in the nodes without using super-convergent points and successive extrapolation to the nodes. With CM approach, balance equations are directly obtained in a discrete form and only global variables are used, thus avoiding energetic functionals and their differentiation in order to find critical points. The consequence is that no limitation is imposed by differentiability conditions. For example, the constitutive matrix may vary freely from one cell to the neighbor, or heterogeneities may be the same size of the discretization. In the paper, Cell Method for elasticity problems is introduced and three node and six node cells are applied to the two-dimensional study of elastic stress distribution in lugs. A three dimensional model with four nodes tetrahedra has also been presented.