The Large Deflection of the Orthotropic and Rectangular Membrane under the External Distributed Load

2012 ◽  
Vol 166-169 ◽  
pp. 725-729 ◽  
Author(s):  
Long Jun ◽  
Zheng Zhoulian ◽  
Liu Changjiang ◽  
Song Weiju ◽  
Yin Hui Zhang ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Perturbation Method ◽  
External Load ◽  
Large Deflection ◽  
Maximum Deflection ◽  
Distributed Load ◽  
Small Deflection

This paper reviews research on the large deflection of the orthotropic and rectangular membrane under the distributed load. Through building the theoretical model of the orthotropic and rectangular membrane under the distributed load, the authors deduce the equations set of the membrane which has the effect of pretension and solve the equations set with the perturbation method. The authors obtain the relational expression between the maximum deflection of the membrane’s centre point and the external load, then make a comparison between the large deflection and the small deflection. At last, With the example, the authors analyze the change of the deflection of the centre point of the membrane along the external load, and the length of the side, and the large or small of the pretension and other parameter.

The Deflection of Orthotropic Saddle Membrane under the Snow Load

2014 ◽  
Vol 624 ◽  
pp. 626-629
Author(s):  
Hong Zeng ◽  
Yin Hui Zhang ◽  
Jun Long
Keyword(s):  
Perturbation Method ◽  
External Load ◽  
Maximum Deflection ◽  
Snow Load

This paper reviews the research on the deflection of orthotropic saddle membrane under the external snow load. First the authors build the model of orthotropic saddle membrane under the snow load. Second we deduce the equations set of the saddle membrane which has the effect of pretension. Then we solve the equations set with the perturbation method. So we obtain the relational expression between the maximum deflection of the membrane’s centre point and the external load. At last, suppose that the load was determinate, the authors analyze the change of the deflection of the centre point of the membrane with different pretensions, side lengths and other parameters.

Research on the Deflection of Membrane Structure under the Snow Load

2014 ◽  
Vol 1065-1069 ◽  
pp. 1222-1225
Author(s):  
Hong Zeng ◽  
Yu Pu ◽  
Jun Long
Keyword(s):  
Perturbation Method ◽  
External Load ◽  
Membrane Structure ◽  
Maximum Deflection ◽  
Snow Load ◽  
Flat Membrane

This paper reviews the research on the deflection of the orthotropic flat membrane and saddle membrane under the external snow load. First the authors analyze the characteristics of snow load and obtain the standard snow load. Second we build the models of the orthotropic flat membrane and saddle membrane under the snow load. Then we deduce and solve the equations set of the two membranes under the effect of the pretension with the perturbation method. So we obtain the relational expression between the maximum deflection of the membrane’s centre point and the external load. At last, suppose that the load was determinate, the authors analyze the change of the deflection of the centre point of the membrane with different pretensions, side lengths and other parameters.

scholarly journals Nonlinear Deflection Model for Corner-Supported, Thin Laminates Shape-Controlled With Moment Actuators

2007 ◽  
Author(s):  
Jordan E. Massad ◽  
Pavel M. Chaplya ◽  
Jeffrey W. Martin ◽  
Philip L. Reu ◽  
Hartono Sumali
Keyword(s):  
Shape Control ◽  
Large Deflection ◽  
Flexible Structures ◽  
Piezoelectric Actuators ◽  
Input Voltage ◽  
Thin Plates ◽  
Small Deflection ◽  
Shape Controlled ◽  
Rectangular Laminate ◽  
Small Deformations

The shape control of thin, flexible structures has been studied primarily for edge-supported thin-plates. For applications such as electromagnetic wave reflectors, corner-supported configurations may prove more applicable since they allow for greater flexibility and larger achievable deflections when compared to edge-supported geometries under similar actuation conditions. Models of such structures provide insight for effective, realizable designs, enable design optimization, and provide a means of active shape control. Models for small deformations of corner-supported, thin laminates actuated by integrated piezoelectric actuators have been developed. However, membrane deflections expected for nominal actuation exceed those stipulated by linear, small deflection theories. In addition, large deflection models have been developed for membranes; however these models are not formulated for shape control. This paper extends a previously-developed linear model for a corner-supported thin, rectangular laminate to a more general large deflection model for a clamped-corner laminate composed of moment actuators and an array of actuating electrodes. First, a nonlinear model determining the deflected shape of a laminate given a distribution of actuation voltages is derived. Second, a technique is employed to formulate the model as a map between input voltage and deflection alone, making it suitable for shape control. Finally, comparisons of simulated deflections with measured deflections of a fabricated active laminate are investigated.

Effect of Ring Beam Stiffness on Behaviour of Reticulated Timber Domes

2005 ◽  
Vol 20 (3) ◽  
pp. 143-160 ◽  
Author(s):  
Dan H. Pan ◽  
Ulf Arne Girhammar
Keyword(s):  
Critical Pressure ◽  
Load Capacity ◽  
Structural Systems ◽  
Maximum Deflection ◽  
Bending Moments ◽  
Normal Forces ◽  
Distributed Load ◽  
Entire Structure ◽  
Global Buckling ◽  
Triangular Network

Domes are efficient structural systems for long clear-span buildings. The introduction of laminated timber highlighted the economic advantages of this material and led to the use of timber domes even for very large spans. In this paper, reticulated timber domes of triangular network shape with decking and bottom tension ring are considered. These types of domes have high stiffness in all directions along the surface and are kinematically stable. The dome is subjected to uniformly distributed load over the entire structure. The dome model is generated with a preprocessor program called DOME-IN and analysed with ABAQUS. The focus of this paper is to evaluate the behaviour of reticulated timber domes with respect to different stiffnesses of the bottom ring beam, here defined as a non-dimensional ring beam area parameter Ar*, which is shown to be a very well adapted design parameter for the ring beam. As far as global buckling is concerned, the critical pressure is sensitive to the bottom ring beam stiffness only if the latter is within a certain range. In terms of design, the stiffness of the ring beam should exceed A* > 2 in order to utilise the full buckling load capacity of the dome system itself. The maximum deflection, normal forces and bending moments versus the ring beam area parameter are also evaluated. The maximum values of the deflection and the internal actions next to the bottom ring are very sensitive to the bottom ring beam stiffness only if the latter is less than about Ar* < 10. A recommended value for the design of the bottom ring beam is A* > 20.

scholarly journals Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
H. Vázquez-Leal ◽  
Y. Khan ◽  
A. L. Herrera-May ◽  
U. Filobello-Nino ◽  
A. Sarmiento-Reyes ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Cantilever Beam ◽  
Homotopy Perturbation Method ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Follower Force ◽  
Homotopy Perturbation ◽  
Solution Methods ◽  
Nonlinear Pendulum

In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to179.99999999∘yielding a relative error of 0.01222747.

A New Driving Principle for Micromechanical Torsional Actuators

1999 ◽  
Author(s):  
Harald Schenk ◽  
Peter Dürr ◽  
Detlef Kunze ◽  
Heinz Kück
Keyword(s):  
Large Deflection ◽  
Deflection Angle ◽  
Characteristic Curve ◽  
Theoretical Description ◽  
Experimental Results ◽  
Electrode Configuration ◽  
Maximum Deflection ◽  
Mechanical Oscillations ◽  
Small Electrode ◽  
Cmos Compatible

Abstract An electrostatic driving principle for micromechanical torsional actuators is presented which allows to excite mechanical oscillations with large deflection angles at low driving voltages. This is achieved by a special electrode configuration which enables the usage of small electrode gaps. The functionality is demonstrated by various 1D-scanner chips which are fabricated in a CMOS-compatible process. When the excitation is synchronized with the oscillation a maximum deflection angle is obtained. For this case a theoretical description of the characteristic curve is given and compared to experimental results. Furthermore, FEM calculations on the deflection dependence of the capacitance are presented.

Impact and Bending of a Rigid-Plastic Fan Blade

1984 ◽  
Vol 51 (3) ◽  
pp. 501-504 ◽  
Author(s):  
W. J. Stronge ◽  
T. Shioya
Keyword(s):  
Centrifugal Force ◽  
Large Deflection ◽  
Impact Force ◽  
Centrifugal Forces ◽  
Transverse Impact ◽  
Rigid Plastic ◽  
The Third ◽  
Small Deflection ◽  
The Difference ◽  
Fan Blade

A rigid-plastic fan blade is subjected to a transverse impact force at the tip in addition to radial centrifugal forces caused by fan rotation. Large and small deflection formulations for inplane bending of the cantilevered blade are calculated and compared. If the effects of centrifugal force are completely considered, the difference between these calculations is shown to be small within the beam. Most of the deflection originates from plastic deformation far from the tip so the large deflection effects near the tip have little influence. The largest curvature is inversely proportional to the centrifugal force, directly proportional to the third power of impact force, and always occurs near the point of impact.

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