Finite Element Analysis $($FEA$)$:

Finite Element Analysis $($FEA$)$ is a powerful numerical technique widely used in civil engineering for analyzing complex structures and predicting their behavior under various loading conditions. Describe the theoretical framework of FEA, including the discretization process, selection of elements, and formulation of the stiffness matrix. Explain the concept of shape functions and their role in interpolating the behavior of elements. Discuss the principles of equilibrium and compatibility governing the solution process in FEA. Additionally, explore the limitations and challenges associated with FEA, such as mesh sensitivity$,$ convergence criteria, and numerical instabilities. Finally, discuss recent advancements in FEA techniques and their implications for civil engineering analysis and design.