This paper presents a polynomial layer-wise model in the framework of Carrera's Unified Formulation for the bending analysis of a magneto-electric shells with variable radii of curvature. A parametric surface is used to model the middle surface of the shell. Lame Parameters and Radius of Curvature are calculated by using Differential Geometry. The mechanical displacement, along with the electric and magnetic scalar potential functions, are expressed and modeled using Chebyshev polynomials of the Second Kind. The shells are exposed to different mechanical, electrical and magnetic loads. The Principle of Virtual Displacement is employed for obtaining the governing equations which are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved in semi-analytical manner by the so-called Differential Quadrature Method (DQM). The basis function selected is the Lagrange polynomial. The DQM is employed for its straightforwardness in tackling complex yet regular shell structures under various multiphysical loads. A simple stress recovery technique based on 3D equilibrium equations is introduced to obtain the out-of-plane shear and normal stresses, transverse electric, and magnetic induction. Close-to-3D solutions have been achieved for classical shell structures. Furthermore, benchmark solutions for complex smart shells featuring variable radii of curvature, such as parabolic and cycloidal shells, are introduced.

中文翻译：

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复杂几何磁电壳的统一分层模型

本文提出了在卡雷拉统一公式框架下的多项式分层模型，用于对具有可变曲率半径的磁电壳进行弯曲分析。参数化曲面用于对壳体的中间曲面进行建模。Lame 参数和曲率半径是使用微分几何计算的。使用第二类切比雪夫多项式来表达和建模机械位移以及电和磁标量势函数。外壳承受不同的机械、电气和磁负载。采用虚拟位移原理来获得控制方程，该控制方程通过切比雪夫-高斯-洛巴托网格分布进行离散化，并通过所谓的微分求积法（DQM）以半解析方式求解。选择的基函数是拉格朗日多项式。DQM 因其在各种多物理载荷下处理复杂而规则的壳结构的简单性而被采用。引入了一种基于 3D 平衡方程的简单应力恢复技术，以获得面外剪切应力和法向应力、横向电感应和磁感应强度。经典壳结构已实现接近 3D 的解决方案。此外，还介绍了具有可变曲率半径的复杂智能壳体（例如抛物线壳体和摆线壳体）的基准解决方案。