New Analytical Method with Curvature Based Kinematic Deflection Curve Theory

Abstract

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.

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

“…If the deflection curve is differentiable, the slope angle of the deflection curve in curvilinear coordinates can be evaluated from (1) just by integration. If the integration begins from a specific reference point where the slope angle is known, the slope angle of the terminal point can be derived from (1) by integrating as follows [15]:…”

“…Exact planar kinematic displacement theory for a non-uniform curvature distribution was first reported with the application of a tapered rectangular elastic cantilever beam subjected to a tip moment [11]. An analytical method for the deflection calculations using curvature values was originally reported with the application of an elastic rectangular tapered beam subjected to a tip moment [15]. Numerical analysis of an elastic perfectly plastic stiffened panel with KDT was presented by Bayraktarkatal and Tayyar [18] and Tayyar et al [19].…”

Assessment of Ultimate Longitudinal Strength of a VLCC considering Kinematic Displacement Theory

“…점진붕괴법(PCM, progressive collapse method)으로 불리기 도 하는 반복증분법은 Smith법 (Smith, 1977)을 기반으로 하고 있으며, 비손상 선박의 선체 강도를 예측하기 위해서 사용되어 왔다 , 1997IACS, 2010aIACS, , 2010b 보강판 평균압축강도에 대한 연구는 Cho, et al (1998), Paik and Kim (2002), Paik and Thayamballi (2002), , Tayyar and Bayraktarkatal (2012) Table 2 Scantling and material 이는 KDT 평균압축강도가 CSR 평균압축강도에 비하여 보수적인 평가를 하기 때문이다 (Fig. 6 참조).…”

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This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents prediction of ultimate longitudinal strength of a VLCC, "Energy Concentration" for which many benchmark studies have been carried out, based on kinematic displacement method proposed by Tayyar and Bayraktarkatal (2012). Kinematic displacement theory provides semi-analytical solution of average compressive strengths for various kinds of stiffened panels.

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“…This paper presents prediction of ultimate longitudinal strength of a VLCC, "Energy Concentration" for which many benchmark studies have been carried out, based on kinematic displacement method proposed by Tayyar and Bayraktarkatal (2012). Kinematic displacement theory provides semi-analytical solution of average compressive strengths for various kinds of stiffened panels.…”