Best upper bounds on strain energy and surface displacements of an elastic body under boundary tractions

Ru, C.
October 2012
Acta Mechanica;Oct2012, Vol. 223 Issue 10, p2197
Academic Journal
This work studies best upper bounds on strain energy and surface displacements of an elastic body under boundary tractions prescribed on its surface. It is found that two best bound constants, defined by two integral inequalities for strain energy and surface displacements, respectively, are equal and can be determined by an eigenvalue problem of linear elasticity characterized by spring-like elastic-boundary conditions with a negative spring constant. Explicit expressions for the best bound constants are derived for a circular body in plane strain and an elastic beam under transverse loading.


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