Structural analysis forms the cornerstone of mechanical engineering design, providing insights into the behavior of materials and components under various loading conditions. Discuss the fundamental principles underlying the finite element method $($FEM$)$ as a numerical technique for solving complex structural problems. Illustrate the key steps involved in the formulation and implementation of FEM, highlighting concepts such as discretization, element types, boundary conditions, and solution strategies. Furthermore, examine the advantages and limitations of FEM compared to analytical and experimental approaches in predicting the mechanical response of structures subjected to static and dynamic loads.