Variational Methods

Abstract

Variational methods involve the use of minimization principles such as the principles of minimum potential energy and minimum complementary energy. These minimization principles can be used to derive governing equations and boundary conditions for specialized classes of problems in elasticity. Another important application of energy methods is in finding approximate solutions to elasticity problems, which involves making assumptions about the relative accuracy of different approximations based on the minimization of certain quantities to be defined. For instance, this is the basis of the numerical algorithm known as the finite element method.