Strong Formulation IsoGeometric Analysis for the vibration of thin membranes of general shape

A strong form finite element technique, termed SFEM, has been presented recently. This approach resulted to be accurate and reliable for different engineering problems. The SFEM merges the high convergence rates of strong form pseudo-spectral methods and the versatility of domain decomposition techniques proper of the Finite Element Method (FEM). The governing differential equations and the compatibility conditions between two adjoining elements are transformed through the mapping technique. Due to its higher order nature given by the collocation of several points in each single element, classic 8 node elements are not often sufficient to map a geometry with the smallest amount of elements. Therefore, a new mapping approach based on blending functions is introduced in this paper for investigating membrane structures. In particular, isogeometric mapping based on Non-Uniform Rational Basis Spline (NURBS) will be considered. This kind of nonlinear mapping is generally associated with Isogeometric Analysis (IGA). Therefore, the present new approach is termed Strong Formulation Isogeometric Analysis (SFIGA). In order to prove the accuracy and stability of this technique several analytical and other results from the literature will be presented together with new applications.