An efficient model reduction method for buckling analyses of thin shells based on IGA

An efficient reduced basis method is proposed for buckling analyses of thin shells subject to large deformations and strains. The thin shells are modeled with the classical Kirchhoff–Love kinematics under the framework of IGA (Isogeometric Analysis), which makes it possible to satisfy the requirement of C¹ continuity. The analytically defined geometry of thin shells can be exactly represented by the NURBS (Non-Uniform Rational B-Splines) basis functions. In addition, the critical buckling point can be better pin-pointed due to the exact geometric description. For efficient structural analyses, a simplified ROM (Reduced Order Model) is presented by combining the Koiter perturbation technique and the finite element method (FEM). Alternative perturbation forces, based on nonlinear eigenvalue analyses, are also proposed. Embedding three strategies including arc-length control, accompanying eigenvalue analysis and mode injection into the analysis procedure, the proposed method is extended to be applicable to nonlinear buckling analyses. Furthermore, imperfection sensitivity analyses can be conveniently performed with the proposed method. Finally, the effectiveness and efficiency of the proposed method are validated via three benchmark problems.