Energy methods

The basic equations of linear elasticity are derived in chapter 1 and are conveniently divided into three groups: the equilibrium equations, the strain-displacement relationships, and the constitutive laws, as illustrated in fig. 9.33. In chapter 9, two virtual work principles are derived. First, the principle of virtual work is established and shown to be entirely equivalent to the equilibrium equations of the system; this principle, however, provides no information about the other two sets of equations, the strain-displacement relationships and constitutive laws, which must be obtained in the traditional manner. Second, the principle of complementary virtual work is established and shown to be entirely equivalent to the strain-displacement relationships of the system; this principle, however, provides no information about the other two sets of equations, the equilibrium equations and constitutive laws, which must obtained in the traditional manner. To remedy this situation, new principles will be developed in this chapter that are entirely equivalent to two of the three groups of equation of linear elasticity. The main tool used to achieve this generalization of the principles presented in chapter 9 is the concept of conservative forces.