A corotational flat shell element for the geometrically nonlinear analysis of laminated composite structures is presented. The element is obtained from the Hellinger–Reissner variational principle with assumed stress and displacement fields. The stress interpolation is derived from the linear elastic solution for symmetric composite materials. The element is isostatic, namely the stress interpolation is ruled by the minimum number of parameters. Displacement and rotation fields are only assumed along the contour of the element. As such, all the operators are efficiently obtained through analytical contour integration. The geometrical nonlinearity is introduced by means of a corotational formulation. The proposed finite element, named MISS-4c, proves to be locking free and shows no rank defectiveness. A multimodal Koiter's algorithm is used to obtain the initial postbuckling response. Results show good accuracy and high convergence rate in the geometrically nonlinear analysis of composite shell structures.

中文翻译：

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一种用于层状复合结构高效几何非线性分析的共旋混合平壳有限元

提出了一种用于层合复合结构几何非线性分析的共旋平壳单元。该单元是根据具有假定应力和位移场的 Hellinger-Reissner 变分原理获得的。应力插值源自对称复合材料的线弹性解。该单元是等静压的，即应力插值由最少数量的参数决定。位移和旋转场仅沿元素的轮廓假设。因此，所有算子都可以通过分析轮廓积分有效地获得。几何非线性是通过共旋公式引入的。所提议的有限元，名为 MISS-4c，证明是无锁定的并且没有显示秩缺陷。多式联运 Koiter' s 算法用于获得初始后屈曲响应。结果表明，复合材料壳结构几何非线性分析具有良好的精度和较高的收敛速度。