ABSTRACT

This chapter summarizes GM/WF for BVPs described by self-adjoint differential operators and present an alternate approach in which the details of the finite element processes can be derived directly without using the fundamental Lemma and integration by parts. While the mathematical basis for the approach presented here remains the same as GM/WF, but the approach presented in the chapter is perhaps more appealing as it deals directly with the physics. The chapter revisits some basic concepts. To maintain consistency with the notation used in linear elasticity, structural mechanics, and energy, the chapter introduces the new notation. It first considers classical methods of approximation. The chapter also presents derivations of the details of finite element formulations for linear structural and linear solid mechanics using the principle of minimum potential energy. It shows that minimization of total potential energy is identical to Galerkin method with weak form for self-adjoint differential operators that are encountered in linear structural and linear solid mechanics.