Static and Dynamic Analyses of Arbitrarily Shaped Laminated Composite Structures

It is well known that many applications in several fields of engineering cannot be solved analytically due to the complexity of the governing equations. Therefore, a particular technique is needed to solve numerically the problem under consideration. As regards the structural analyses, the most common approach is the Finite Element Method (FEM), which decomposes the domain in several subdomains and finds an approximate solution evaluating the equations in their weakened form. On the other hand, the authors have developed a different approach which solves the governing equations in their strong form using a higher order numerical scheme inside each element. The so-called collocation methods based on the distribution of points upon the physical domain is employed to discretize the partial differential system of governing equations. Since the domain decomposition in several elements characterizes both the two approach, the presented technique can be termed Strong Formulation Finite Element Method (SFEM) in order to stress the fact that it is based on the strong formulation. The SFEM expresses all its potentiality especially when an irregular domain is considered. In fact, most of the practical applications in civil, mechanical and aerospace engineering are quite hard to analyze due to the presence of irregular geometries, different kind of materials, cracks, curved boundaries and load discontinuities. Several structural applications are shown to demonstrate convergence, reliability and stability of the SFEM when it is applied to the static and dynamic analyses of arbitrarily shaped laminated composite plates, membranes and beams with geometrical and mechanical discontinuities.