An efficient isogeometric buckling optimization framework for multi-patch laminated shells: Leveraging 3D solid elements, lamination parameters and penalty method

Buckling is a common failure mode of laminated shell structures during service, and isogeometric analysis methods are highly suitable for the buckling analysis due to their accurate geometric modeling capability and high-order continuity. However, the isogeometric buckling analysis for a multi-patch structure and its optimal design still face challenges in computational efficiency. To address this issue, this paper proposes an integrated framework for the buckling optimization of multi-patch laminated shells, which leverages 3D solid elements, lamination parameters, and the penalty coupling method. Solid-shell elements have advantages in shell analysis due to their simplicity, absence of rotational degrees of freedom, and adaptive layering in the thickness direction. Lamination parameters simplify the optimization of fiber orientations in laminated shells by condensing the design variable space and improving the convexity of the optimization problem. The penalty method can handle the coupling in multiple patches at a relatively low cost. Nevertheless, lamination parameters are rarely applied to the case of solid-shell elements. In addition, despite using lamination parameters, the number of design variables for multi-patch structures remains significantly large. To tackle these issues, this study derives the solid-shell formulation in lamination parameters and the sensitivity analysis formulae in the reverse mode. Experiment validation is conducted to assess the accuracy of the proposed method based on lamination parameters with solid elements, the feasibility of the multi-patch optimization model, and the computational efficiency of optimization sensitivity based on the reverse mode compared to the forward counterpart common in the literature.