Finite Deformation of 2-D Curved Beams with Variable Curvatures

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. also investigated the stability of nonlinear equilibrium equations for fluid pressure loading. Due to the complexity of mathematical models, analytical solutions are very limited. Timoshenko [14] showed the large deformation of an elastica. It also showed the stability of a straight beam of large deformation. In this paper, we apply the tangent slope coordinate theory by Lin [15,16,17] to study finite deformation 2-D of curved rods with variable curvatures.

Analysis of finite deformation of curved beams bonded with piezoelectric actuating layers

“…But Atanackovic, Brush and Almroth restricted their research only on curved beams. Lin et al (2009) used Lagrangian description together with Eulerian description to derive the analytical solutions of curved beams with variable curvatures. The bending and point force loads were all considered.…”