Abstract
An analytical method is derived for obtaining the finite deformation of 2-D thin curved beams with variable curvatures. The general solutions are expressed by fundamental geometric quantities. As the radius of curvature is given, the fundamental geometric quantities can be calculated to obtain the closed form solutions of the axial force, shear force, bending moment, rotation angle, and deformed and un-deformed displacement fields. The closed-form solutions of the circular, spiral, ellipse, parabola, cycloid, catenary and logarithmic spiral beams under pure bending moment cases and simple circular curved beam under a pair of horizontal forces are presented. The results show the consistency in comparison with ANSYS results.
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