Comment on the Navier's solution in 'A sinusoidal beam theory for functionally graded sandwich curved beams' (Composite Structures 226 (2019) 111246)

摘要

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.