Exact solution considering layerwise mechanics for laminated composite and sandwich curved beams of deep curvatures

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.