Anisotropic solid-like shells modeled with NURBS-based isogeometric approach: Vibration, buckling, and divergence analyses

Abstract

We proposed an IGA formulation for free vibration, buckling and divergence analyses of generally anisotropic solid-like composite shells. Recently developed Rayleigh–Ritz based methods are not accurate enough for curved shells since they are not able to capture twisting mode shapes. Here, we use the advantages of isogeometric analysis (IGA) and develop a three-dimensional higher-order continuous solid-like shell (SLS) model. Since the continuity of material orientation is crucial in numerical analysis of anisotropic shells, non-uniform rational B-splines (NURBS) are used to establish a smooth interpolation through the thickness and on the middle surface of the shell for both the geometry and displacement fields. The developed isogeometric SLS is coupled with Bézier extraction operators to represent continuity between multi-patch anisotropic domains. Numerical solutions for composite laminated shells with different boundary conditions are compared with analytical solutions or other solutions from the literature. In this context, we study the influence of span-to-thickness ratios, different shapes, modulus ratios, member aspect ratios and various layouts on the mechanical response. With the presented model, we were able to obtain the twisting mode shapes, which are not frequently observed in orthotropic and isotropic ones. We also study the influence of the polynomial order of the IGA formulation on the results.