Explore the theoretical framework and computational methodologies underlying finite element analysis $($FEA$)$ in the context of structural engineering. Examine the fundamental principles of FEA, including discretization techniques, element formulations, and solution algorithms, while elucidating its applicability in modeling and analyzing complex structural systems subjected to various loading conditions. Furthermore, discuss the practical considerations, numerical challenges, and validation strategies associated with FEA simulations to ensure accurate and reliable predictions of structural behavior and performance.