The closed-form compliance equations for combined-parabola-shaped flexure hinge based on the unit-load method

2015 ◽  
Author(s):  
Qiang Li ◽  
Dong Liu
Keyword(s):  
Closed Form ◽  
Flexure Hinge ◽  
Unit Load ◽  
Unit Load Method

EVALUATION OF MOUNTAIN AREA AS NON-POINT SOURCE OF NITROGEN FOR SETO INLAND SEA: THE NORTHERN SHIKOKU REGION, JAPAN

2017 ◽  
Author(s):  
Shohei Morisawa ◽  
Shohei Morisawa ◽  
Yukio Komai ◽  
Yukio Komai ◽  
Takao Kunimatsu ◽  
...  
Keyword(s):  
Average Concentration ◽  
Point Sources ◽  
Seto Inland Sea ◽  
Mountain Streams ◽  
Unit Load ◽  
Mountain Areas ◽  
Mountain Area ◽  
The Seto Inland Sea ◽  
Unit Load Method ◽  
Important Position

The northern Shikoku region is located in the Western part of Japan and faces towards the Seto Inland Sea. The forest area, which is one of the non-point sources in the Seto Inland Sea watershed, occupies 75% of the land use in the watershed of the northern Shikoku region. The amount of loadings of nutrients and COD in the Seto Inland Sea has been estimated by the unit load method but actually the data has not been investigated. It is however, necessary to know the real concentration of nitrogen in mountain streams to evaluate the role which is the mountain area plays as non-point sources. Therefore, more water samples of mountain streams in the watershed need to be taken and the concentrations of nitrogen analyzed. The mountain streams in the northern Shikoku area were investigated from April, 2015 to November, 2015. The number of sampling sites was 283, in addition to the past data by Kunimatsu et al. The average concentration of nitrate nitrogen in Ehime, Kagawa, and Tokushima was 0.61mg/L, 0.78mg/L and 0.34mg/L, respectively. The environmental standard range for nitrogen in the Seto Inland Sea is from between less than 0.2mg/L and less than 1mg/L. Therefore, the average concentration of nitrogen in these regions was over category II, and those of mountain streams in Kagawa Prefecture exceeded category III. About 20% of mountain streams were more than 1mg/L. It has become clear that mountain areas occupy an important position as non-point sources for the Seto Inland Sea.

Corner-Filleted Flexure Hinges

2000 ◽  
Vol 123 (3) ◽  
pp. 346-352 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Jeffrey S. N. Paine ◽  
Ephrahim Garcia ◽  
Michael Goldfarb
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Finite Element Simulation ◽  
Analytical Approach ◽  
Flexure Hinge ◽  
Closed Form Solutions ◽  
Flexure Hinges ◽  
Element Simulation ◽  
Model Predictions ◽  
The Right

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

A Method for Design of Oblique Intersection Beams in Roof Structures

2011 ◽  
Vol 211-212 ◽  
pp. 827-831
Author(s):  
Tao Zhang
Keyword(s):  
Cross Section ◽  
Design Method ◽  
Effective Cross Section ◽  
Vertical Displacement ◽  
Unit Load ◽  
Compatibility Equation ◽  
Unit Load Method ◽  
Beam Section ◽  
Set Up ◽  
Node Position

To facilitate calculation of a reinforced concrete oblique intersection beams in roof structures, the analysis ignores the interaction between moment and torque of node position, assuming the beam ends as hinge supports. Vertical displacement coefficients were found out by unit-load method, the compatibility equation of displacement was set up by the conditions of equal displacement at nodes, which can finally calculate force diagram of beams, and further design beam section. When designing, it is necessary to note reinforcement calculation should be taken into account the change of beam effective cross-section high caused by longitudinal tension reinforcement layer placed. Compared with the engineering example show that the design method is more simple and accurate, the results can provide a reference for the engineering design and related research.

Performance Analysis of a Hyperbolic Flexure Hinge Based on its Closed-Form Equations

2011 ◽  
Vol 421 ◽  
pp. 540-543 ◽  
Author(s):  
Jun Feng Hu ◽  
Pei Li ◽  
Xiang Fu Cui
Keyword(s):  
Closed Form ◽  
Size Range ◽  
Structural Parameters ◽  
Small Variation ◽  
Flexure Hinge ◽  
Small Range ◽  
Accuracy Analysis ◽  
Flexible Hinge ◽  
Sensitivity Equations ◽  
Out Of Plane

In order to the effects of structural sizes of a hyperbolic on its performance, sensitivity and accuracy analysis are performed in this paper. According to the structure feature and force exerted on the flexible hinge, the closed-form equations are formulated for compliances to characterize both the active rotation and all other in- and out-of-plane parasitic motions by using the Castigliano’s second theorem. Meanwhile, the accuracy equations are obtained using the Castigliano’s second theorem. According to the closed-form flexibility formulas, the effects of the four structural parameters, such as thickness, notch depth, length and width, on the flexibility of flexible hinge are analyzed, respectively. In order to study further the effects of the structural parameters on its flexibility, we derive the sensitivity equations, and the sensitivity analysis is carried out. Meanwhile, the accuracy analysis of the hyperbolic flexure hinge is performed. The analysis results have shown that the parameters have large influence on in-plane compliance, and have small effects on out-of-plane one. And the changes are larger within initial small range of parameters, while be small variation in larger size range. And the length has no effect of sensitivity.

Closed-Form Equations of Mass Matrix of the Single-Axis Right Circular Flexure Hinge

2009 ◽  
Author(s):  
Xianmin Zhang ◽  
Wenfeng Hou ◽  
Yisheng Guan
Keyword(s):  
Dynamic Analysis ◽  
Closed Form ◽  
Compliant Mechanism ◽  
Mass Matrix ◽  
Closed Form Expression ◽  
Flexure Hinge ◽  
Analysis Model ◽  
Form Expression ◽  
Positioning Stage ◽  
The Right

This paper presents a closed-form expression of the mass matrix of the right circular hinges which are widely used in compliant mechanism systems. The flexure hinge is treated as a two nodes element, in which there are three degrees of freedom at each node. The cosine functions with high-order terms are introduced, and the closed-form expression for each element of the mass matrix of the single-axis right circular flexure hinge is obtained. Based on the closed-form expression, the dynamic equations of motion of a piezodriven 3-DOF compliant precision micro-positioning stage are developed. The lower order modal frequencies are experimentally identified and the dynamic analysis model is proved to be feasible. Dynamic and static output comparisons show that the dynamic analysis is highly necessary for a precision micro-positioning stage. The closed-form expression of the mass matrix of the right circular hinge made it more convenient for dynamic analysis of the compliant mechanisms by using finite element approach.

Bearing Capacity Analysis for Statically Indeterminate Attachment System of Tower Crane Considering Single Limb Instability

2013 ◽  
Vol 446-447 ◽  
pp. 463-468
Author(s):  
Nian Li Lu ◽  
Shu Rui Wen
Keyword(s):  
Local Buckling ◽  
Internal Force ◽  
Calculation Model ◽  
Critical Force ◽  
Unit Load ◽  
Tower Crane ◽  
Unit Load Method ◽  
Internal Forces ◽  
Attachment Device ◽  
The Moment

The tower cranes need constantly attaching to rise in the construction of high-rise buildings. The tower body which sets attached frames combined with the four-rod-type unilateral statically indeterminate attachment system is a common form. With the attachment height and distance increasing, the attachment rods become more delicate and flexible. It is necessary to check the overall and local stability of the attachment structure. When a single limb instability happens, the reduced-order variation structure brings about the redistribution of internal forces. The anti-buckling capability depends on the structure of variation. To the condition that the single limb instability occurrs on the component which has the weakest stiffness, an exact internal force expression of the structure under composite loads has been deduced in terms of the moment equilibrium method. At the same time, the decoupling support stiffnesses of the attachment device in each direction have been obtained by the unit load method. Based on the refined calculation model, the internal forces are further analyzed under the condition that the instability rod bears the fixed Euler critical force, and the structural strength and stability capacity has been judged. The calculation result proves that the whole structure has great bearing potential after a local buckling.

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