Abstract In this work, a third-order efficient layerwise theory (ELWT) has been developed for laminated composite and sandwich curved beams of deep curvatures. The circumferential displacement is assumed to have global third-order variation in thickness (radial) coordinate with a linear layerwise variation. The number of independent variables is reduced to 3 by imposing the continuity of displacement and transverse shear stress at interfaces and shear free conditions on the outer and inner surfaces. Equations of the motion are derived using Hamilton’s principle. Navier type analytical solution is obtained for simply supported ends. Results for static deflection, stresses, and natural frequencies are presented for laminated composites and sandwich curved beams of different radii of curvature and thicknesses. The importance of inclusion of the deepness terms ( 1 + z / R ) in the formulation for the static and free vibration responses are discussed by comparing with the exact 2D elasticity solution. It is shown that the results predicted by the present ELWT are more accurate than equivalent single layer theories having same number of variables. For sandwich curved beams, the predictions of third-order theory (TOT) are extremely poor in comparison with ELWT. The results presented in the paper will be useful for assessing the accuracy of other simplified 1D theories.

中文翻译：

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考虑分层力学的深曲率夹层复合材料和夹层弯曲梁的精确解

摘要 在这项工作中，已经为深曲率的层压复合材料和夹层弯曲梁开发了三阶有效分层理论（ELWT）。假设圆周位移在厚度（径向）坐标中具有全局三阶变化，并具有线性分层变化。通过在界面处施加位移和横向剪切应力的连续性以及在外表面和内表面上施加无剪切条件，自变量的数量减少到 3。运动方程是使用汉密尔顿原理推导出来的。获得了简支端的 Navier 型解析解。给出了不同曲率半径和厚度的层压复合材料和夹层弯曲梁的静态挠度、应力和固有频率的结果。通过与精确的 2D 弹性解决方案进行比较，讨论了在静态和自由振动响应公式中包含深度项 (1+z/R) 的重要性。结果表明，本ELWT预测的结果比具有相同数量变量的等效单层理论更准确。对于夹心曲梁，三阶理论 (TOT) 的预测与 ELWT 相比非常差。论文中提出的结果将有助于评估其他简化的一维理论的准确性。结果表明，本ELWT预测的结果比具有相同数量变量的等效单层理论更准确。对于夹心曲梁，与ELWT相比，三阶理论（TOT）的预测极差。论文中提出的结果将有助于评估其他简化的一维理论的准确性。结果表明，本ELWT预测的结果比具有相同数量变量的等效单层理论更准确。对于夹心曲梁，与ELWT相比，三阶理论（TOT）的预测极差。论文中提出的结果将有助于评估其他简化的一维理论的准确性。