The closed form general solutions of 2-D curved laminated beams of variable curvatures

The closed form general solutions of in-plane static laminated curved beams of variable curvatures are derived. All the quantities of axial force, shear force, radial and tangential displacements are decoupled and expressed as harmonic functions in terms of angle of tangent slope. The first and second moments of laminated curved beams with respect to x- and y-axes are defined as fundamental geometric properties. The curved beams can be any curve. Some closed form solutions of non-circular laminated beams, rings are presented. Applications of elliptic, parabola, catenary, cycloid, and exponential spiral laminated curved beams are shown. The laminated circular ring under point load and distributed load are studied as well. Two kinds of laminate (0/θ) and (θ/−θ) are investigated in this paper. Effects of aspect ratio, thickness ratios, orthotropy ratios and stacking sequence on the laminated ring are presented. Results of isotropic curved beams are compared with existed solutions. The results are consistent.