Irregular planar polar elements for stress analysis of complex systems having contact surfaces rotating members and interference fits

Abstract

Planar polar triangular and quadrilateral stress elements with polar joint freedoms and their element matrices for general forms of shape functions are developed for the stress and deformation analysis of complex planar elastic systems, especially those having contact surfaces between members, rotating machine members and interference fits. Joint freedom irregularities are introduced to permit non-polar sliding joint freedoms on the non-polar contact surfaces, and permit non-polar force applications. Shape functions used permit higher order variations of stresses within the elements as compared to their cartesian counter parts. Three numerical examples (a curved beam, a layered curved vehicle spring and a rotating wheel) illustrate the efficiency and applications of these elements, where some result are compared with those of photoelasticity solutions. Finally article develops method for the stress analysis of complex systems having single or multiple interference fits, where the external loading and the normal interference distributions along the contact surfaces are known, but the contact pressures and the radial displacements of the contact joints on the inner and outer members of the fits are not known. Four additional numerical examples investigate stresses and deformations in elastic systems having single and multiple interference fits, where the results for fits of concentric cylinders are compared with those of exact elasticity solutions. Digital computer programs are made available for the interested reader.