A NURBS-based degenerated stiffener element for isogeometric static and buckling analysis

Abstract

Complex shells and curvilinear stiffeners are promising for the lightweight design of aerospace structures. Along with the increasing of structural size and geometric characteristics, traditional finite element analysis (FEA) requires fine grids to content the analysis accuracy, which is extremely time-consuming. In this study, a novel NURBS-based degenerated stiffener element is proposed. Based on the 6 degree of freedom (DOF) degenerated beam element, the proposed stiffener element solves the issue of direct coupling between the beam element and 5 DOF degenerated shell element. Skin and stiffener are characterized by NURBS surface and curve, respectively. Meanwhile, the buckling behavior of stiffened panels is investigated based on isogeometric analysis (IGA), which reduces the geometric discrete error and realizes the integration of modeling and analysis. In addition, since the grids of skin and stiffeners are always unmatched, a strong coupling method based on NURBS interpolation and projection algorithm is constructed to merge non-conforming grids. The degrees-of-freedom (DOFs) of stiffeners is eliminated in the equilibrium equation, which greatly reduces the calculation scale. Furthermore, an improved point-to-surface projection algorithm is proposed, which improves the computational efficiency and solves the problem of unstable convergence of Newton iteration. Finally, the static and buckling analyses are performed for different types of stiffened plates and shells. Displacement solutions, von Mises stress solutions and buckling modes are discussed in detail. The prediction accuracy and meshes are compared with the shell-type model and beam-shell-type model in ABAQUS software, which indicates the high applicability and efficiency of the proposed analysis method for various types of stiffened panels.