Classification of Variational Principles in Elasticity

In this paper, variational principles in elasticity are classified accordiag to the differences is the constraints used in these principles, It is shown in a previous paper^[4] that the stress-strain relations are the constraint conditions in all these variational principles, and can not be removed by the method of liaear Lagrange multiplier.The other possible constraats are four of them:(1)equations of equilibrium,(2)Strain-displacement relations,(3)boundary conditions of given external forces and boundary conditions of given boundary displacements. In variational principles of elasticity, some of them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variational principles, However, for every possible variatioaal prineiple, either the strain energy density,or the complementary energy density may be used, Hence, there are altogether 3p classes of functionals of variational principles in elasticity. In this paper, all these functionals are tabulated in detail.