Fatigue and fracture are the terms associate with the mechanical properties of the material. It is majorly concerned with the reliability of the structures. The performance of materials and structural components regardless of scale and geometry. In structural engineering, in addition to metaheuristic optimization algorithms, attention must be paid to the type of materials used in the structures. The materials play an important role in the design of the structure. In the field of structural engineering significant advancement has been carried out in the development of Finite Element Methods (FEM). Obtaining the mechanical properties of metallic plates under complicated conditions is a tedious task. Refined finite element models are useful in situations where accuracy and efficiency cannot be maintained. One of the notable refined FEM is the Carrera Unified Formulation (CUF) which introduced to demonstrate the theoretical model of plate thickness expansion. It is established by using Taylor series expansion and Lagrange series expansion. The governing differential equations of metallic plate are introduced by using the principle of virtual displacements, the mass matrix and stiffness matrix of plate elements. However, this model is not feasible for thick plates. In addition to metallic plates, the high-fidelity modeling of reinforced structures using one-, two-, and three-dimensional elements has become crucial.