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Structural Engineering and Mechanics
  Volume 24, Number 2, September30 2006, pages 155-180

Optimal shape design of contact systems
F. F. Mahmoud, A. G. El-Shafei and M. M. Al-Saeed

    Many applications in mechanical design involve elastic bodies coming into contact under the action of the applied load. The distribution of the contact pressure throughout the contact interface plays an important role in the performance of the contact system. In many applications, it is desirable to minimize the maximum contact pressure or to have an approximately uniform contact pressure distribution. Such requirements can be attained through a proper design of the initial surfaces of the contacting bodies. This problem involves a combination of two disciplines, contact mechanics and shape optimization. Therefore, the objective of the present paper is to develop an integrated procedure capable of evaluating the optimal shape of contacting bodies. The adaptive incremental convex programming method is adopted to solve the contact problem, while the augmented Lagrange multiplier method is used to control the shape optimization procedure. Further, to accommodate the manufacturing requirements, surface parameterization is considered. The proposed procedure is applied to a couple of problems, with different geometry and boundary conditions, to demonstrate the efficiency and versatility of the proposed procedure.
Key Words
    contact mechanics; shape optimization; mathematical programming; surface parameterization; finite element method.
Department of Mechanical Engineering, Zagazig University, Zagazig, 44511, Egypt

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