Abstract
This work is inspired to achieve an integral inequality for a linear elastic body in which the surface integral of squares of surface strains or surface displacement gradients is bounded from above by surface integral of squares of boundary tractions with a finite bound constant independent of boundary tractions. Here, all candidate displacements of the proposed variational quotients are required to meet the equations of equilibrium without body forces, and the boundary tractions are defined based on the displacements. Detailed results are given for two-dimensional anti-plane shear and plane-strain of circular domains, which confirm that the integral of surface strains or surface displacement gradients can be bounded from above by the integral of boundary tractions.
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