Collapse mechanisms and the existence of equilibrium solutions for masonry bodies

Abstract

The equilibrium equations of no-tension (masonry-like) bodies are analyzed. Unlike the existing proofs of the existence of the solution by Anzellotti or Giaquinta and Giusti, the present proof does not employ the uniform safe load condition. It is based on the assumption of the absence of a suitably defined collapse mechanisms. The collapse mechanism belongs to a generalized space BD(cl Ω) of displacements of bounded deformation on the closure cl Ω of the body Ω. This generalized displacement can have a jump discontinuity on the boundary of the body and the generalized strain is a measure on the closure of the body (instead of the standard interpretation as a measure supported by the interior). The equilibrium solution, however, belongs to the classical space of displacements of bounded deformation BD(Ω).