Kinematic Displacement Theory of Planar Structures

Abstract

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.

A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment

“…The curvature values of the cross sections of the beamcolumn are uniform for the segment length ds. The resultant forces on the segment are constant, or the segment is infinitesimal [11]. The shape of the segment for uniform curvature distribution is indicated by the arc of a circle with radius r (figure 4).…”

“…This study examined a new advanced step by adapting elasto-plastic behavior to curvature-based kinematic displacement theory (KDT) [11]. In KDT, deflection is generated precisely without making any geometric assumptions or using differential equations of the deflection curve.…”

New Analytical Method with Curvature Based Kinematic Deflection Curve Theory

“…On the other hand, there is an alternative model that the deflection curve is generated geometrically where the deflection curve consists of circular arcs of osculating circles [1].…”

“…The solutions will more accurate because there is no geometrical assumption like in nonlinear deflection theory or large deflection theory, and will also be faster because only pre-prepared curvature diagrams or functions can be used in simple equations without the need to solve differential equations. In addition to the numerical approximation from theory, where the structure was divided into sections [1], a new analytical method is proposed.…”

“…Therefore, it models the deflection curve with an arc length parameterization whose direction and radius are determined from the curvature values. In theory, there is only one unit tangent vector [2] and only one unit normal vector for a common point of two adjacent arcs [1].…”