As a widely used structural form, doubly-curved composite shells have been applied in aviation and other engineering fields. With a refined mechanical model, structural performances can be accurately predicted to help designers choosing best geometrical and material parameters. This work introduces a novel rectangular finite element for doubly-curved laminated composite shells based on a new set of strain-based shape functions. The governing equations are established on the Mindlin shell theory (a type of first order shear deformable shell theory), which incorporates a rectification of shear correction factor for laminates and von Kármán type nonlinearity. Based on strain approach, the shape functions for rectangular element are assumed as polynomial of 28 parameters to consider the influence of shear effect. Apart from 20 geometrical relations of four element nodes, shear force equilibrium equations are introduced to offer the additional eight equations to derive a new set of shape functions for finite element model. Using shape functions, a novel rectangular shell element is proposed for doubly curved laminated shell, which also maintains a compatibility with Kirchhoff shells. Numerical results for linear static bending, dynamic vibration and nonlinear bending cases of flat plate, cylindrical shell and doubly-curved laminated shell are compared with the available results in literatures and ABAQUS simulation for the sake of validating the present method.

双曲面复合壳体作为一种应用广泛的结构形式，已在航空等工程领域得到应用。借助完善的机械模型，可以准确预测结构性能，帮助设计人员选择最佳几何和材料参数。这项工作基于一组新的基于应变的形状函数，为双弯曲层压复合壳引入了一种新型矩形有限元。控制方程建立在 Mindlin 壳理论（一种一阶剪切变形壳理论）的基础上，该理论包含对层压板和 von Kármán 型非线性的剪切校正因子的修正。基于应变方法，矩形单元的形状函数被假定为28个参数的多项式，以考虑剪切效应的影响。除了4个单元节点的20个几何关系外，还引入了剪力平衡方程，提供了额外的8个方程，以推导出一套新的有限元模型形状函数。使用形状函数，提出了一种新的矩形壳单元，用于双弯曲层压壳，它也保持与基尔霍夫壳的兼容性。为了验证本方法的有效性，将平板、圆柱壳和双曲叠层壳的线性静态弯曲、动态振动和非线性弯曲情况的数值结果与文献和ABAQUS模拟中的可用结果进行了比较。提出了一种新的矩形壳单元用于双弯曲层合壳，它也保持与基尔霍夫壳的兼容性。为了验证本方法的有效性，将平板、圆柱壳和双曲叠层壳的线性静态弯曲、动态振动和非线性弯曲情况的数值结果与文献和ABAQUS模拟中的可用结果进行了比较。提出了一种新的矩形壳单元用于双弯曲层合壳，它也保持与基尔霍夫壳的兼容性。为了验证本方法的有效性，将平板、圆柱壳和双曲叠层壳的线性静态弯曲、动态振动和非线性弯曲情况的数值结果与文献和ABAQUS模拟中的可用结果进行了比较。