ABSTRACT
This chapter introduces some energy techniques and demonstrates that how these techniques are derived, how they are used in mechanics, and how they lead to the numerical solution of the physical quantities that are associated with a particular problem. It examines the mathematical technique of the calculus of variations. The chapter explores the concept of the virtual energy function as the important expression in structural mechanics. It identifies the relevant functional that, when minimized, would lead to the exact solution of the problem. A minimization procedure will yield only an approximate solution to the physical problem. The variational approach in this field is presented along with the minimization processes that are required for deriving the governing equations. The three major fields in Mechanical Engineering are structures, heat transfer, and fluid flow. The chapter addresses the minimization processes associated with heat transfer.
