Stability and Critical Points in Large Displacement Frictionless Contact Problems
The present lecture notes discuss discrete mechanical structures that when deformed may come into frictionless unilateral contact with rigid obstacles. Since arbitrarily large displacements are considered, the structures may buckle, i.e. exhibit instabilities. Classically, for a structure not subjected to unilateral contact, critical points (where the stability behaviour of the structure may change character or bifurcation may occur) are divided into limit points and (smooth) bifurcation points. The presence of contact constraints is shown to introduce additional types of critical points, which we may label as non-smooth bifurcation points, corner limit points and end points.
KeywordsContact Force Bifurcation Point Linear Complementarity Problem Solution Path Unilateral Contact
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