Composite Structures of Arbitrary Shape by Using Nonlinear Isogeometric Mapping

Composite structures have been widely used in several engineering applications nowadays. Their use is mainly in advanced components at all scales from small to large, such as in bio medical engineering and civil and aerospace engineering. In the former body parts are involved in the design process, whereas in the latter large roof and fuselages are studied for industrial applications. Since the 1950s several numerical methods have been introduced to study such structures, most of these techniques were related to weak form finite element methods wherein the variational form of the governing equation is analyzed. Unfortunately, such numerical schemes might have numerical issues due to geometry approximation and convergence behavior. For solving such problems strong form numerical approaches were introduced in order to have higher accuracy trends and “almost exact” geometry approximation since such scheme is based on collocation points. Among all the recent developed strong form techniques the Differential Quadrature (DQ) method has been deeply investigated in the last years. However, the DQ method can only be applied to geometries of regular shape such as domains in Cartesian, polar or orthogonal curvilinear coordinates. In order to be able to generalize such approach the mapping technique and the domain decomposition method must be introduced. The authors developed a strong form finite element technique which considers Not Uniform Rational B-Splines (NURBS) to described geometrically the edges of the elements within the given mesh. Such curves are taken from CAD software so that the resulting geometric approximation of the physical structure is more accurate and flexible than other classic mapping approaches.