Finite Elements: Elasticity and Variational Formulation

This lecture covers the application of finite element methods to solve elasticity problems, focusing on variational formulations and numerical implementations. Topics include finite differences, Galerkin method, and finite element schemes. The instructor discusses the formulation of weak variational problems and the method of Galerkin, emphasizing the importance of admissible deformations and the space of admissible functions. The lecture also explores the concept of symmetric matrices and the uniqueness of solutions. Practical examples and numerical solutions are presented to illustrate the theoretical concepts.