An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotropic and multilayered shells with different geometrical configurations and boundary conditions, including the case of a non-smooth geometry. Comparisons with analytical solutions and finite-element simulations show the high-order accuracy as well as the capability and robustness of the proposed formulation, which can be a valuable tool for the analysis of generally-curved multilayered shells.

在这项工作中提出了多层壳弹性分析的原始公式。该公式的主要特征是： 通过曲线坐标的通用系统表示壳平均表面；通过基于位移场协变分量的全厚度扩展的等效单层方法对一般壳理论的统一处理；以及求解控制方程组的内罚不连续伽辽金方案。这些特征的组合使用使得多层壳问题的高阶解成为可能。针对具有不同几何配置和边界条件的各向同性、正交各向异性和多层壳，包括非光滑几何的情况，提出了几种数值试验。