Shape optimal design of bodies in elastic contact

Many problems in mechanical design involve elastic bodies that come into contact under an applied load. Contact deformations and stresses depend as much on geometric profiles of the contacting bodies as on the externally applied forces. Desired contact conditions can thus be attained through proper design of the initial contour or shape of the contacting bodies. In this thesis, an integrated approach is presented for the shape optimal design of bodies in elastic contact. This approach will find applications in various engineering problems such as cylindrical and tapered fits, orthotics, fir-tree joints, electrical contacts, metal and elastomeric seals, cams, gears and bearings.; In practical contact problems, the geometry of the region of contact is far too irregular for analytical solutions to be feasible. A point-to-cubic numerical sliding contact algorithm is developed in this thesis, in order to perform contact analysis of complex geometries. This algorithm, which is based on the finite element method, is tested for accuracy by comparing it with standard Hertz contact solutions and the commercial nonlinear finite element codes.; Contact shape optimization requires the identification of suitable objective functions for minimization. Various formulations for the objective function are discussed and the most effective are chosen. Parametrization of the shape of the contacting bodies and effective generation of specialized velocity fields for contact shape optimization are described in detail. A technique to explicitly control interpenetration of the geometry of the contacting bodies is developed. The technique is based on determining a maximum limit on the step size during the line search phase of the optimization. Issues relating to the differentiability of the objective and constraint functions in the design space are discussed along with special procedures for numerical design sensitivity analysis.; The shape optimizer is interfaced with the point-to-cubic sliding contact algorithm. The resulting contact shape design logic is applied to the solution of engineering problems. Applications are limited to two-dimensional plane stress, plane strain and axisymmetric problems.