What are the underlying principles and considerations behind the application of the finite element method in structural analysis within civil engineering? Discuss its mathematical foundation, including the formulation of stiffness matrices and load vectors, and elucidate how these are utilized to solve complex structural problems. Furthermore, delve into the various types of finite elements commonly employed, such as beam, truss, and shell elements, and expound upon their respective advantages and limitations$.$ Additionally, analyze the significance of convergence criteria in ensuring the accuracy and reliability of finite element solutions, and elucidate the iterative procedures involved in achieving convergence. Lastly, explore the role of software tools in facilitating finite element analysis and assess their effectiveness in simulating real$-$world structural behavior.