Abstract
This paper investigates the collapse of rigid assemblies under applied forces, by using a two-dimensional model of contacting rigid discs. Expansions are made rigorously for both the frictionless and the Coulomb-frictional contacts, respectively. For the frictionless assemblies, some existing mathematical theorem and an associated calculation procedure are introduced, which are precisely applicable to their mechanics. As for the frictional assemblies, by employing new decompositions of a contact force and its relative displacement, conjugate to each other, and by showing the existence of frictionless rigid assemblies of another kind with common static conditions to them, it is concluded that the limits of their static equilibria do not coincide with the collapse initiations.
