Abstract In “A sinusoidal beam theory for functionally graded sandwich curved beams” (Composite Structures 226 (2019) 111246), the Navier’s solution was obtained for a so-called simply-supported curved beam at two ends. However, this case is mathematically indeterminate and hence not worked out. Based on the Timoshenko theory, the governing differential equations are formulated for curved beam problems and then analytically solved. Excellent agreement with the elasticity theory validates the solution for a free-clamped curved beam. Careful study on the simply-supported curved beam shows that the Navier’s solution in the literature is the one when the inappropriate constraint is assumed, which causes a significant error (up to 42%) for a relative large-curvature beam. In this paper, the Navier’s solution is therefore assessed.

中文翻译：

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评纳维尔在“功能梯度夹层弯曲梁的正弦梁理论”中的解决方案（复合结构226（2019）111246）

摘要 在“功能梯度夹层曲梁的正弦梁理论”（Composite Structures 226 (2019) 111246）中，获得了所谓两端简支曲梁的纳维解。然而，这种情况在数学上是不确定的，因此没有解决。基于 Timoshenko 理论，针对弯曲梁问题制定控制微分方程，然后进行解析求解。与弹性理论的极好一致性验证了自由夹紧弯曲梁的解决方案。对简支曲梁的仔细研究表明，文献中的 Navier 解是假设约束不当时的解，这会导致相对大曲率梁的显着误差（高达 42%）。在本文中，因此评估了 Navier 的解决方案。