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A new contact analysis algorithm by shape optimization (CASO) has been proposed: A sequence of usual elasticity problems is solved iteratively until the unknown contact and stick regions are converged while minimizing the mismatches in the contact and friction conditions. It is based on the continuous LCP (linear complementarity problem) formulation of the contact. A series of examples with known solutions or without are solved for verification and show simplicity and beauty of the unique method.
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Kwak et al. (2009) studied this question.
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