This paper presents a new curvature based kinematic displacement theory and a numerical method to calculate the planar displacement of structures from a geometrical viewpoint. The theory provides an opportunity to satisfy the kinematic equilibrium of a planar structure using a progressive numerical approach, in which the cross sections are assumed to remain plane, and the deflection curve was evaluated geometrically using the curvature values despite being solved using differential equations. The deflection curve is parameterized with the arc-length, and was taken as an assembly of the chains of circular arcs. Fast and accurate solutions of most complex deflections can be obtained with few inputs.
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.
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