Static Analysis of Curved Beams with Clamped-Clamped Ends under Thermo Load

2011 ◽  
Vol 117-119 ◽  
pp. 1543-1546
Author(s):  
Xiao Fei Li ◽  
Chun Yi Cui ◽  
De Hai Yu
Keyword(s):  
Thermal Expansion ◽  
Static Analysis ◽  
Cross Section ◽  
Analytical Solutions ◽  
Virtual Work ◽  
Curved Beams ◽  
Curved Bridges ◽  
Internal Forces ◽  
The Cross ◽  
Scientific Base

Based on the principle of thermal expansion and theory of virtual work, a class of equations for in-plane displacements at three freedom direction and internal forces in the cross-section of statically indeterminate curved beams under thermo load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

Analytical Solutions at Three Freedom Direction for Curved Beams with Clamped-Pinned Ends under Thermal Load

2011 ◽  
Vol 94-96 ◽  
pp. 322-325
Author(s):  
Xiao Fei Li ◽  
Ying Hua Zhao ◽  
De Hai Yu
Keyword(s):  
Thermal Expansion ◽  
Cross Section ◽  
Analytical Solutions ◽  
Thermal Load ◽  
Virtual Work ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Internal Forces ◽  
Scientific Base

The purpose of the paper is to present analytical solution of curved beam with clamped-pinned ends under thermo load based on the principle of thermal expansion and theory of virtual work. A class of equations for in-plane displacements at three freedom direction and internal forces in the cross-section of statically indeterminate curved beams under thermo load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

Exact Radial Displacement Solutions of Curved Beams with Clamped-Clamped Ends

2012 ◽  
Vol 178-181 ◽  
pp. 2164-2167
Author(s):  
Xiao Fei Li ◽  
Zhe Fu Yu ◽  
Chun Yang Zhu ◽  
Chen Chen
Keyword(s):  
Cross Section ◽  
Analytical Solutions ◽  
Radial Displacement ◽  
Radial Direction ◽  
Virtual Work ◽  
Curved Beams ◽  
Curved Bridges ◽  
Concentrated Load ◽  
Internal Forces ◽  
Scientific Base

Based on the principle of thermal expansion and theory of virtual work, a class of equations for in-plane displacements at radial direction and internal forces in the cross-section of statically indeterminate curved beams under radial concentrated load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

Exact Solutions of Dynamic Characteristics for Curved Beams with Pinned-Pinned Ends

2013 ◽  
Vol 405-408 ◽  
pp. 702-705
Author(s):  
Xiao Fei Li ◽  
Wei Ming Yan ◽  
Hao Xiang He
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
Stiffness Matrix ◽  
Virtual Work ◽  
Analytic Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Scientific Base

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. Basing on the stiffness matrix of statically indeterminate curved beams at three freedom direction, the dynamic characteristics are derived explicitly. The analytic method of dynamic characteristics for curved beam performed in this paper would provide a scientific base for further study and design of the curved bridges.

Exact Solutions of Stiffness Matrix for Curved Beams with Pinned-Pinned Ends

2011 ◽  
Vol 368-373 ◽  
pp. 3117-3120
Author(s):  
Xiao Fei Li ◽  
Ying Hua Zhao ◽  
Chun Yang Zhu ◽  
Chen Chen
Keyword(s):  
Exact Solutions ◽  
Analytical Solutions ◽  
Stiffness Matrix ◽  
Virtual Work ◽  
Curved Beams ◽  
Curved Bridges ◽  
Thermal Elasticity ◽  
Scientific Base

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The stiffness matrix of statically indeterminate curved beams at three freedom direction is derived explicitly. The exact solutions of stiffness matrix obtained in this paper would provide a scientific base for further study and design of the curved bridges

scholarly journals Determining reaction forces in planar mechanisms

2009 ◽  
Vol 31 (1) ◽  
pp. 57-64
Author(s):  
Do Sanh ◽  
Dinh Van Phong ◽  
Do Dang Khoa ◽  
Phan Dang Phong
Keyword(s):  
Cross Section ◽  
Constraint Forces ◽  
Planar Mechanisms ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Internal Forces ◽  
The Cross ◽  
Joint Reaction

In the paper, it is introduced a method to determine joint reaction forces, constraint forces and internal forces at the cross section of linkages. Based on the principle of compatibility and the ideality of constraints, the methodology is presented to analyze and determine reaction forces in planar mechanisms.

scholarly journals Developing a Formulation Based upon Curvature for Analysis of Nonprismatic Curved Beams

2007 ◽  
Vol 2007 ◽  
pp. 1-19
Author(s):  
H. Saffari ◽  
M. J. Fadaee ◽  
R. Tabatabaei
Keyword(s):  
Cross Section ◽  
Arbitrary Point ◽  
Polar Coordinate System ◽  
Stationary Condition ◽  
Curved Beams ◽  
Total Potential ◽  
Polar Coordinate ◽  
The Cross ◽  
The Relationship ◽  
Deformation Relationship

A new element with three nodal curvatures has been considered for analysis of the nonprismatic curved beams by finite element method. In the formulation developed, the force-curvature relationships in polar coordinate system have been obtained first, then the curvature of the element has been assumed to have a second-order polynomial function form and the radial, tangential displacements, and rotation of the cross section have been found as a function of the curvature accounting for the effects of the cross section variation. Moreover, the relationship between nodal curvatures and nodal deformations has been calculated and used for determining the deformations in terms of curvature at an arbitrary point. The total potential energy has been calculated accounting for bending, shear, and tangential deformations. Invoking the stationary condition of the system, the force-deformation relationship for the element has been obtained. Using this relationship, the stiffness matrix and the equivalent fixed loads applying at the nodes have been computed. The results obtained have been compared with the results of some other references through several numerical examples. The comparison indicates that the present formulation has enough accuracy in analysis of thin and thick nonprismatic curved beams.

scholarly journals The method of determining internal forces at any cross section of links in mechanisms

2004 ◽  
Vol 26 (2) ◽  
pp. 110-121
Author(s):  
Do Sanh ◽  
Do Dang Khoa
Keyword(s):  
Cross Section ◽  
Analytical Mechanics ◽  
Equilibrium Equations ◽  
Closed Loops ◽  
Equal Zero ◽  
Mechanical Constraints ◽  
Reaction Forces ◽  
Internal Forces ◽  
The Cross

In the paper it is introduced a method of determining internal forces at any cross section of the links of mechanisms. As known, so far it is used the method of D'Alembert, which consists of two steps, the determination of the acceleration states of links and the establishment of the equilibrium equations for the set of forces including the forces of inertia and the internal forces at the cross section. A. I. Lurie proposed a method of analytical mechanics for this problem. Its concept is to make a new system called the released one by cutting the link at a cross section under consideration and adding some coordinates. Only one condition putting restriction on the released system is the additional coordinates must equal zero. Under this restriction the new created system is coincided to the original one. This restriction is equivalent to put the mechanical constraints, whose reaction forces are the components of internal forces at the cross section under consideration. It is necessary emphasize that the Lurie's method is convenient only for opened loops, but is not applied for closed ones. Moreover, the Lagrange's multiplier equations applied by A. I. Lurie are unsuitable. In this paper it is presented the generalized Lurie's method, which is applied for the opened and closed loops by using the Principle of Compatibility.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Energy Distribution in Electron Beams

1972 ◽  
Vol 30 ◽  
pp. 568-569
Author(s):  
Tamotsu Ohno
Keyword(s):  
Electron Beam ◽  
Energy Distribution ◽  
Cross Section ◽  
Integral Curve ◽  
Electron Beams ◽  
Electron Gun ◽  
Angular Divergence ◽  
Apparent Increase ◽  
Integral Width ◽  
The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

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