Isogeometric Analysis of Composite Structures Through Mapping Using Blending Functions

The Differential Quadrature (DQ) method is a numerical technique for the solution of initial and boundary value problems. It is well-known that this method has been applied to a variety of physical and engineering problems through the years. As almost any numerical approach, the DQ method can be easily used in regular domains, such as squares and rectangles. In very recent years, the authors extended this limitation introducing the Strong Formulation Finite Element Method (SFEM) which merges the advantages of DQ method and a mapping technique using serendipity elements. However, mapping through serendipity elements can lead to errors related to geometry approximation. For example, when an 8-node element is used to map an arc of circumference. This mapping is not exact except at the nodal points at the boundaries. These kind of difficulties can be avoided by using blending functions that allow exact mapping. For the sake of generality, the authors considered Non Uniform Rational Basis-Splines (NURBS) as blending functions for the nonlinear mapping of any general element into the computational space. NURBS are curves widely used in the CAD design and they are usually used for the geometric description of structural components. The aim of this study is to investigate the structural behavior of composite structures where discontinuities and curved boundaries are present. Numerically speaking the convergence, reliability and stability on the static and dynamic solutions lead by the SFEM are shown through practical applications related to civil, mechanical, aerospace and naval engineering.