On a Class of Conservation Laws in Linearized and Finite Elastostatics.

摘要

The investigation was prompted by Rice's (1968) discovery of a path-independent integral appropriate to two-dimensional elastostatic fields in the presence of infinitesimal deformations. It is shown that Rice's conservation law,as well as its three-dimensional counterpart,may be generated systematically by means of a known theorem on invariant variational principles in conjunction with the principle of stationary potential energy. Further,this procedure yields two additional conservation laws of the same type. According to a completeness theorem established here,the scheme alluded to above cannot give rise to conservation laws beyond those cited already,as far as the fully linearized theory is concerned. Finally,two of the three laws deduced in this paper,when suitably reinterpreted,are found to hold rigorously in the nonlinear equilibrium theory of hyperelastic solids. The results obtained promise to be of practical value in connection with the direct asymptotic analysis of geometrically induced singular stress concentrations. (Author)