New Analytical Method with Curvature Based Kinematic Deflection Curve Theory

  • Tayyar, Gokhan Tansel
  • Received : 2012.06.11
  • Accepted : 2012.08.07
  • Published : 2012.08.31


This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.


Curvature;Deflection curve;Tapered beam;Displacement


  1. G.T. Tayyar and E. Bayraktarkatal, "Kinematic Displacement Theory of Planar Structures". International Journal of Ocean System Engineering. 2(2) (2012), 63-70.
  2. B.A. Barsky and T.D. DeRose, "Geometric Continuity of Parametric Curves: Three Equivalent Characterizations". IEEE Computer Graphics & Applications. 9(6) (1989), 60-68.
  3. G.E. Hay, "The Finite Displacement of Thin Rods". Trans. Am. Math. Soc. 51 (1942), 65-102.
  4. M. Berger and B. Gostiaux, Differential Geometry: Manifolds, Curves, and Surfaces. New York: Springer, (1988).
  5. J.M. Gere and S.P. Timoshenko, Mechanics of Materials, fourth ed. Boston: Pws, (1997).