On a class of conservation rules associated with sensitivity analysis in linear elasticity
The authors discuss a new class of conservation laws and path-independent integrals. This class is associated with variation of arbitrary stress, strain and displacement functionals due to infinitesimal translation, rotation or scale change of an inhomogeneity within the elastic body. The analysis is limited to linearly elastic material within small strain theory. In {\S} 2 the general expressions for variation of arbitrary volume of surface integrals of stress, strain and displacement due to boundary variation are derived and the concept of an adjoint body is introduced. In {\S} 3 the respective conservation rules are proved for the case of linear elasticity and small strain theory. In {\S} 4 the transition to path-independent integrals associated with potential and complementary energy variation can be obtained by specifying the adjoint systems and using the previous general expression for variations. In {\S} 5 the conservation rules for bilinear functionals are generated as singular cases of the previous general case assuming localized force or dislocation action on the adjoint body, whereas in {\S} 6 some possible applications are indicated.
scientific article; zbMATH DE number 4009903