Abstract
This contribution contains description of modelling technique of contact problems of bodies with curved surfaces when assumption of infinitesimal displacements can be considered to give sufficient accuracy for both displacement and stress analysis. This assumption considers that the local configuration of the bodies in contact will not be influenced during the deformation process and only dimensions and shape of the contact surfaces and contact pressures will change by the load conditions. Such assumptions enable to reduce the contact problem considerably, if the local contact displacement and stress fields are modelled as local fields inside large elements (sub-domains) using superposition of a local Hertz type field and a smooth field modelled in a classical way using large FEM or BEM technique. A technique of obtaining the complex solution of the bodies in contact as a combination of the local contact field defined by the Boussinesq's solution and the smooth field modelled by multi-domain BEM is described and considered to be a basis for the modelling and design of contact problems containing large gradient displacements.
Highlights
If spherical bodies in contact have much different curvatures at least in one direction, like it is in roller bearings, the contact area is very small and under normal loading the contact pressure may occur in order of several thousand N/ mm2
The stiffness matrix of the T-elements is obtained by integration over the element boundaries, which enables to conserve the cylindrical form of the contact surfaces in the computational models
This is important for the accurate enough definition of rolling contact elements for the multibody contact problems like the rolling bearings as described in our previous model [15], in which, classical FE model using fine mesh was used to model the local fields
Summary
If spherical bodies in contact have much different curvatures at least in one direction, like it is in roller bearings, the contact area is very small and under normal loading the contact pressure may occur in order of several thousand N/ mm. In each case, it is assumed that the topology of each contact surface does not change with the load and the contact element for the global model is considered to be 1D with the stiffness obtained from the 2D characteristic containing the dependence of the resulting force direction. In this way the contact characteristics can be obtained from the local model and the complex multibody contact can be modelled by large elements, which leads to considerable saving of computational time and computer memory. The methodology used in this approach is not restricted to the contact problems of the bodies with curved surfaces, but can be used in some modifications to other problems like cracks inside the bodies or on their surface, small inclusions and inhomogenities, etc., i.e. all problems, in which the local effects cause large gradients in the displacement and stress fields
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