Optimization techniques for contact stress analysis.
McDonald, Eric S.
Kwon, Young W.
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The analysis of stresses induced by contact between two bodies is inherently difficult because the size of the contact zone is unknown and constantly changing throughout loading. To overcome these difficulties, two approximation methods have been developed to determine the magnitude of contact stresses using the Rayleigh-Ritz method and the finite element method. Numerical optimization methods are employed to solve the contact problem. The solution techniques are compared to known analytical solutions and shown to yield accurate results. An application of this approach to solving the contact problem is illustrated by examining the response of a clamped sandwich composite beam to low velocity impact. It was found that the maximum shear stress is insensitive to lamina thickness, however an increase in the contact layer thickness resulted in a reduction in interfacial shear stress. In addition, it was noted that a nonlinear bending stress distribution in the contact layer intensified as the thickness of this layer increased. This phenomenon was found to be localized to the region of contact. Finally, it was found that the compressive transverse normal stresses increased as the thickness of the contact lamina increased.
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