A simplified isogeometric approach for vibrational analysis of nanocomposite panels with a free-form curve. (February 2023) - Mohammadi, Hassan; Shojaee, Mohammad; Kiani, Yaser
Abstract: This paper investigates, the free vibration behavior of nanocomposite panels with a free-form curve slides on a straight line. It is assumed that the laminated composite panel is fabricated from two phases: polymeric matrix and graphene platelets (GPLs) as a reinforcement in a way that the weight fraction of GPLs varies from layer-to-layer. The equation of motions of the panel are presented using the curvilinear coordinate system in conjunction with the Kirchhoff–Love shell assumptions. In the next step, a novel and simplified procedure have been introduced to discretize the weak form equation by using B-spline basis functions. In other words, there is no need to calculate weight coefficients in the presented methodology. Consequently, the discretization procedure yields simple transformation equations which can be employed for a general singly curved panel with an arbitrary profile. The numerical results are validated for elliptic, parabolic and quartic panels with those generated by ABAQUS as well as cylindrical panels with those available in the open literature. After that, an extensive set of results are obtained as benchmark solutions to study the influences of geometrical and material parameters on the vibrational behavior of the nanocomposite panels. Highlights: Removing of the weight coefficients in geometry representation via a unique determination of a set of control points. Applying B-spline basis functions to generate the geometry of an arbitrary curve. The usage of B-spline basis functions to reduce computational cost in comparison with NURBS basis functions. Parametric study of the free vibration analysis of singly curved panels with arbitrary cross sections. Studying the fast convergence of the proposed technique.