ABSTRACT
This chapter presents key principles that are related to or directly involve variational approaches. Specifically, the principles of virtual work and complementary virtual work, and from these respectively derive the principles of total potential energy and total complementary energy. The chapter explores Reissner's principle and also presents certain functionals and shows that the corresponding Euler-Lagrange equations are of critical importance in solid mechanics. It deals with a differential equation and establish the functional for which the equation is the Euler-Lagrange equation. The chapter shows that the key equations of structural mechanics and elasticity have self-adjoint and positive definite operators for all physically meaningful boundary conditions. It investigates the process of varying in some way the stress field and external forces while holding displacement fields fixed. The chapter provides to work with the functional for the purpose of finding approximate solutions to the corresponding differential equation.
