Large deflections of a spring-hinged tapered cantilever beam with a rotational distributed loading

1987 ◽  
Vol 91 (909) ◽  
pp. 429-437 ◽  
Author(s):  
B. Nageswara Rao ◽  
G. Venkateswara Rao
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Large Deflection ◽  
Rectangular Cross Section ◽  
Large Deflections ◽  
Elastic Curves ◽  
Distributed Load ◽  
Tapered Cantilever Beam ◽  
Large Deflection Problem ◽  
Special Case

SummaryLarge deflection problem of a spring loaded hinged nonuniform cantilever beam subjected to a rotational distributed loading is formulated by means of a second-order non-linear integro-differential equation. The problem is examined by considering the beam of rectangular cross-section with linear depth taper subjected to a uniform rotational distributed load. The elastic curves of a beam for this special case are presented.

scholarly journals Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

2016 ◽  
Vol 10 (1) ◽  
pp. 23-37 ◽  
Author(s):  
Alberto Borboni ◽  
Diego De Santis ◽  
Luigi Solazzi ◽  
Jorge Hugo Villafañe ◽  
Rodolfo Faglia
Keyword(s):  
Differential Equation ◽  
Cantilever Beam ◽  
Cross Section ◽  
Large Deflection ◽  
External Action ◽  
Constant Load ◽  
Large Deflections ◽  
Eulerian Method ◽  
Vertical Displacements ◽  
Newton Raphson

The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The problem is nonlinear due to the constitutive model and to the large deflections. The associated computational problem is related to the solution of a set of equation in conjunction with an ODE. An approximated approach is proposed here based on the application Newton-Raphson approach on a custom mesh and in cascade with an Eulerian method for the differential equation.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

scholarly journals A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

The shape of a Möbius band

1993 ◽  
Vol 440 (1908) ◽  
pp. 149-162 ◽  
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Solution ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Rods ◽  
Large Deflections ◽  
Mechanical Equilibrium ◽  
Elastic Rod ◽  
Flexible Material ◽  
Möbius Band

The shape of a Möbius band made of a flexible material, such as paper, is determined. The band is represented as a bent, twisted elastic rod with a rectangular cross-section. Its mechanical equilibrium is governed by the Kirchhoff–Love equations for the large deflections of elastic rods. These are solved numerically for various values of the aspect ratio of the cross-section, and an asymptotic solution is found for large values of this ratio. The resulting shape is shown to agree well with that of a band made from a strip of plastic.

Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

2017 ◽  
Vol 17 (08) ◽  
pp. 1750091 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Constant Volume ◽  
Large Deflections ◽  
Buckling Loads ◽  
Geometrical Nonlinear ◽  
Deflection Theory ◽  
Large Deflection Theory

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

scholarly journals Calculation of wooden beams on the stability of a flat bending shape enhancement

2018 ◽  
Vol 196 ◽  
pp. 01003 ◽  
Author(s):  
Anton Chepurnenko ◽  
Vera Ulianskaya ◽  
Serdar Yazyev ◽  
Ivan Zotov
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Stability Problem ◽  
Secular Equation ◽  
Rectangular Cross Section ◽  
Center Of Gravity ◽  
Critical Force ◽  
Distributed Load ◽  
Matlab Package ◽  
The Stability

Flat bending stability problem of constant rectangular cross section wooden beam, loaded by a distributed load is considered. Differential equation is provided for the cases when load is located not in the center of gravity. The solution of the equation is performed numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the Matlab package. A relationship between the value of the critical force and the position of the load application point is obtained. A linear approximating function is selected for this dependence.

Proposing a Pretwisted Bending Actuator

Aerospace ◽  
2006 ◽  
Author(s):  
Frank Dienerowitz ◽  
Nicole Gaus ◽  
Wolfgang Seemann
Keyword(s):  
Magnetic Fields ◽  
Cross Section ◽  
Large Deflection ◽  
Mechanical Energy ◽  
Electric Energy ◽  
Small Strain ◽  
Large Deflections ◽  
Direct Transformation ◽  
Active Elements ◽  
Bending Actuator

Piezoelectric bending actuators take advantage of both piezoelectricity and kinematics of beams, i.e. (1) direct transformation of electric energy into mechanical energy without causing significant magnetic fields and (2) to be capable of turning small strain modifications into large deflections, provided the cross-section is rather flat. Unfortunately the latter usually implies that bending actuators provide only one axis of large deflection. Herein a pretwisted bending actuator is investigated, similar to a helicoid. The active elements along the beam axis are subdivided and controlled separately, hence allowing independent control of the curvature of each section. Due to the pretwist, this bending actuator can provide not only one but two axes of deflection. For a slender pretwisted bending actuator the problems emerging are presented and discussed, covering the work space of the actuator, optimization of electrode connecting patterns and experimental results.

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