Contact, Friction, Discrete Mechanical Structures and Mathematical Programming
These lecture notes contain three main parts. The first part is the mathematical modeling of the discrete finite-dimensional, small displacement, quasistatic, frictional contact problem.
The second part contains four sections, where four different contact problems are formulated as Linear Complementarity Problems (LCPs): the frictionless problem, the steady sliding problem, the rate problem and the incremental problem. These are all derived from the quasistatic problem formulated in the first part. The four problems are discussed with respect to existence and multiplicity of solutions.
The third and final part of the lecture notes concerns structural optimization in contact problems. We go through the main peculiarities related to optimum mechanical design of structures involving unilateral frictionless contact and give examples of results obtained for the so called gap design problem.
KeywordsContact Force Contact Problem Linear Complementarity Problem Normal Contact Force Quasivariational Inequality
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