Fundamentals of Finite Element (FE) Method

This course covers the comprehensive understanding of stress analysis, finite element method (FEM), nonlinearity in finite element modeling, and elastoplastic behavior in finite element analysis. It starts with the relationship between stress, strain, and displacement in three-dimensional elements, and how finite elements are modeled using potential energy minimization. The course then moves on to the application of FEM in heat transfer problems and the use of the weighted residue technique in finite element-based formulation. It further delves into the concept of nonlinearity, explaining how properties such as thermal conductivity, specific heat, and viscosity can change with temperature, leading to nonlinearity. The course concludes with the concept of elastoplastic behavior in finite element analysis, focusing on the application of this concept in thermomechanical models associated with welding fusion processes. An example used in this course is the analysis of a brick element, which is a type of three-dimensional element.