Explore the intricate principles and methodologies behind structural analysis in civil engineering. Discuss how the theoretical frameworks of equilibrium, compatibility, and material constitutive laws integrate to form the backbone of structural analysis. Explain the significance of the method of joints and the method of sections in determining the internal forces of a structure, and how these methods are applied to analyze both statically determinate and indeterminate structures. Additionally, delve into the role of finite element analysis $($FEA$)$ in modern structural engineering, elaborating on how FEA is used to simulate complex structures under various loading conditions. Consider how advancements in computational power and software development have influenced the accuracy and efficiency of structural analysis. Reflect on the challenges faced when modeling real$-$world conditions theoretically, including considerations of non$-$linearity, dynamic loading, and material anisotropy. How do these challenges impact the safety and reliability of civil engineering projects?