Explain the principles behind finite element analysis $($FEA$)$ in civil engineering and its significance in structural analysis. Discuss how FEA aids in predicting the behavior of complex structures under various loading conditions, including static, dynamic, and thermal loads. Elaborate on the mathematical formulations and numerical methods involved in FEA, such as mesh generation, element types, and solution techniques. Furthermore, delve into the advantages and limitations of FEA compared to analytical methods and experimental testing in civil engineering applications. Evaluate the role of FEA in optimizing designs, assessing structural integrity, and ensuring safety standards in civil engineering projects, emphasizing its importance in modern engineering practice.