Mechanics of Arbitrarily Shaped Composite Structures Using Isogeometric Mapping

Recently it has been proven that differential quadrature can be applied to arbitrarily shaped structures through mapping technique. This general approach has been termed by the authors Strong Formulation Finite Element Method (SFEM) in contrast with standard weak formbased element methods. The most common approach uses serendipity Lagrangian functions such as the ones used in Finite Element (FE) analysis. Due to its higher order accuracy, the main advantage of differential quadrature within domain decomposition is that the domains can be larger. Thus, serendipity elements are not always suitable to map element edges of general shape. For this reason, the authors employ blending functions to map a general shape element in the computational space. For the sake of generality, the blending functions are not defined case by case, but they are descripted using Non Uniform Rational Basis-Splines (NURBS). The use of NURBS, which are the most common tool used in CAD design, reduces the error carried out through mapping from a general shape domain into a regular one. Therefore, the authors merged the versatility of differential quadrature for studying engineering problems in strong formulation, such as the mechanics of composite structures and the major advantage of nonlinear mapping using NURBS, locating the present approach in the framework of isogeometric analysis. The convergence, reliability and stability of the SFEM is demonstrated through several practical applications mainly related to composite structures.