Finite Element Method: Weak Formulation and Applications

This lecture covers the integral and weak formulations of the problem in the context of the Finite Element Method (FEM). It discusses the equilibrium equations, boundary conditions, and the gallerkin method for approximate weak formulations. The instructor explains the application of FEM to one-dimensional problems, including the discretization process and the solution of linear systems. Additionally, it explores the use of elementary stiffness matrices and vectors, as well as the condensation of stiffness matrices. The lecture concludes with practical examples demonstrating the application of FEM to solve engineering problems involving discontinuities and varying boundary conditions.