Mechanical Characteristics of Origami Mechanism Based on Thin Plate Bending Theory

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Yu Hongying ◽  
Guo Zhen ◽  
Zhao Di ◽  
Liu Peng
Keyword(s):  
Thin Plate ◽  
Mechanical Characteristics ◽  
Superposition Principle ◽  
Bending Moment ◽  
Deflection Curve ◽  
Paper Surface ◽  
Geometric Characteristics ◽  
Small Deflection ◽  
Thin Plate Bending ◽  
The Relationship

This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab, and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve.

The Application of Iteration and Functional Analysis in Numerical Calculation of Beams with Large Deformation

2011 ◽  
Vol 243-249 ◽  
pp. 6144-6149
Author(s):  
Jing Yan ◽  
Ya Wu Zeng ◽  
Rui Gao
Keyword(s):  
Mathematical Modeling ◽  
Functional Analysis ◽  
Bending Moment ◽  
Steady State Solution ◽  
Vertical Displacement ◽  
Axial Deformation ◽  
Governing Equations ◽  
Deflection Curve ◽  
Initial Value ◽  
Small Deflection

For the research of beam’s deformation, material mechanics uses equation of small deflection curve which neglects 1storder derivative of deflection and regards bending moment M is merely a function of abscissa x, and then gets the approximate solution of vertical displacement. However in some case, small deflection curve isn’t efficacious, so two methods come up in this paper to solve the accurate differential equation of beam’s deformation. This paper takes a slightness beam from temperature controlling device as an example and shows detailed process of mathematical modeling and solving. For iteration, firstly governing equations are founded, then an initial value is put into it to work out a new value, next see the new value as a new initial value and calculate again, by doing the operation repeatedly steady-state solution will be got in the end. For functional analysis, deflection equation is assumed as a kind of function containing some undetermined coefficients, then make it satisfy all the boundary conditions, and establish residual fonctionelle, by partial derivative operation to make the fonctionelle minimum, undetermined coefficients are estimated and deflection curve is got. At the end, impacts of gravity and axial deformation are discussed.

Transverse Young's Moduli and Cell Shapes in Coniferous Early Wood

Holzforschung ◽  
2002 ◽  
Vol 56 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ugai Watanabe ◽  
Minoru Fujita ◽  
Misato Norimoto
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Bending Moment ◽  
Cell Models ◽  
Young’S Moduli ◽  
Cell Shapes ◽  
The Difference ◽  
Square Cells ◽  
Experimental Values ◽  
The Relationship

Summary The relationship between transverse Young's moduli and cell shapes in coniferous early wood was investigated using cell models constructed by two dimensional power spectrum analysis. The calculated values of tangential Young's modulus qualitatively explained the relationship between experimental values and density as well as the difference in experimental values among species. The calculated values of radial Young's modulus for the species having hexagonal cells agreed well with the experimental values, whereas, for the species having square cells, the calculated values were much larger than the experimental values. This result was ascribed to the fact that the bending moment on the radial cell wall of square cell models was calculated to be small. It is suggested that the asymmetrical shape of real wood cells or the behavior of nodes during ell deformation is an important factor in the mechanism of linear elastic deformation of wood cells.

The Behavior of Long Beams Under Impact Loading

1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust
Keyword(s):  
Plastic Deformation ◽  
Cross Sections ◽  
Constant Velocity ◽  
Bending Moment ◽  
Infinite Length ◽  
Longitudinal Impact ◽  
Deflection Curve ◽  
Transverse Impact ◽  
Cold Rolled ◽  
Annealed Copper

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.

Required Linepipe Properties for High Strain Applications and Possible Resolution by Pipe Manufacturing Technology

2008 ◽  
Author(s):  
Hitoshi Asahi ◽  
Eiji Tsuru
Keyword(s):  
Tensile Strain ◽  
Compressive Strain ◽  
Bending Moment ◽  
Uniaxial Tensile ◽  
Buckling Behavior ◽  
Strain Limit ◽  
Bent Pipe ◽  
Uniaxial Tensile Stress ◽  
The Relationship ◽  
Pipe Manufacturing

Application of strain based design to pipelines in arctic or seismic areas has recently been recognized as important. So far, there has been much study performed on tensile strain limit and compressive strain limit. However, the relationship between bending buckling (compressive strain limit) and tensile strain limit has not been discussed. A model using actual stress strain curves suggests that the tensile strain limit increases as Y/T rises under uniaxial tensile stress because a pipe manufacturer usually raises TS instead of lowering YS to achieve low Y/T. Under bending of a pipe with a high D/t, an increase in compressive strain on intrados of a bent pipe at the maximum bending moment (ε-cp*) improves the tensile strain limit because the tensile strain limit is controlled by the onset of buckling or ε-cp* which is increased by lowering Y/T. On the other hand, under bending of a pipe with a low D/t, the tensile strain limit may not be influenced by improvement of buckling behavior because tensile strain on the extrados is already larger than the tensile limit at ε-cp*. Finally, we argue that the balance of major linepipe properties is important. Efforts other than the strict demands for pipe properties are also very important and inevitable to improve the strain capacity of a pipeline.

scholarly journals CALCULATION OF THE BENDING ELEMENTS WITH ALLOWANCE FOR THE PHYSICAL NONLINEARITY OF THE STRAIN

2016 ◽  
Vol 1 (12) ◽  
pp. 58-64
Author(s):  
Шишов ◽  
Ivan Shishov ◽  
Рязанов ◽  
Maksim Ryazanov ◽  
Рощина ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Bending Moment ◽  
Physical Nonlinearity ◽  
Deflection Curve ◽  
Physical Strain ◽  
Concrete Condition ◽  
The Finite Difference Method ◽  
Limiting Value ◽  
Small Spacing

An algorithm of the reinforced binding elements calculation with allowance for the physical strain of concrete and reinforcement has been suggested. The three linear diagram of the concrete condition and the two linear of the tensile reinforcement that correspond to the recommended norms in Russia have been used. The task has been solved by the method of linear approximation. The finite difference method has been used at each approximation that allows to define the beam rigidity individually for each dot j =1,2 , dotted on the beam with some small spacing. A method of determining the deflection curve bending, the bending moment, the rigidity as well as the compression areas of the reinforcement suitable for any deformation of the concrete most tensile fabric from 0 to limiting value ε_b2 has been suggested. A solution for the continuous three-span beam has also been introduced.

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