Mechanical Behavior of Laminated Composite Shells with Arbitrary Domains: Comparison Between Weak and Strong Formulations

Several applications in many engineering fields need particular structural elements characterized by arbitrary and distorted geometries. Therefore, accurate and reliable tools must be developed to deal with these problems. In fact, it is well-known that the description of arbitrarily shaped geometries represents a challenging issue of the applied mechanics. These difficulties are even more evident if a laminated composite doubly-curved shell is considered [1, 2]. The main purpose of this research is to present a valid numerical tool to analyze the mechanical behavior of these structures. In particular, the differential geometry is used to evaluate the geometric parameters of the shells. Then, a mapping procedure based on the application of NURBS is introduced to describe distorted domains, following the framework of the Isogeometric Analysis (IGA). An enriched displacement field is employed to take into account several Higher-order Shear Deformation Theories (HSDTs) in a unified manner to have a more accurate analysis of the structural behavior. The governing equations are obtained through the Hamilton’s principle for both the strong and weak formulations. The governing differential equations are changed into a system of discrete equations if the strong formulation is considered, whereas an integral statement is introduced for the weak form. The results of the analyses are carried out by means of the Generalized Differential Quadrature (GDQ) method and the Generalized Integral Quadrature (GIQ) technique [3], respectively. The acronyms SF-IGA (Strong Formulation Isogeometric Analysis) and WF-IGA (Weak Formulation Isogeometric Analysis) are introduced to define such techniques. Several examples and applications are presented to prove the accuracy and reliability of these approaches in dealing with different geometries, lamination schemes, and boundary conditions. The validity of the current methodology is tested by the comparison with the results available in the literature or obtained through three-dimensional finite element models.