Analysis of an Orthotropic Plate by Maclaurin's Series

1963 ◽  
Vol 67 (626) ◽  
pp. 126-127 ◽  
Author(s):  
N. R. Rajappa ◽  
D. V. Reddy
Keyword(s):  
Cross Section ◽  
Orthotropic Plate ◽  
Practical Applications ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Distributed Load ◽  
Functions Of Two Variables ◽  
Uniformly Distributed Load ◽  
Rectangular Orthotropic Plate

A method is presented for the analysis of a simply-supported rectangular orthotropic plate subjected to a uniformly distributed load by the application of Maclaurin's series. The solutions have practical applications in the design of interconnected beam systems because of the elastic equivalence of the grid framework to an orthotropic plate.The application of Maclaurin's series to the analysis of beams in bending was first described by Hetényi. Recently Reddy and Gangadharan described a modified approach for beams with stepped variations in cross section. Ballesteros has extended the method to functions of two variables in the analysis of isotropic plates in bending.

Correlation Between some Stability Problems for Orthotropic and Isotropic Plates under Bi-Axial and Uni-Axial Direct Stress

1954 ◽  
Vol 4 (1) ◽  
pp. 83-92 ◽  
Author(s):  
W. H. Wittrick
Keyword(s):  
Axial Compression ◽  
Orthotropic Plate ◽  
Isotropic Plate ◽  
List Type ◽  
Simply Supported ◽  
Side Ratio ◽  
Buckling Stress ◽  
Isotropic Plates ◽  
Stress Coefficient ◽  
Rectangular Orthotropic Plate

SummaryFour buckling problems are considered, namely: — (a) A rectangular orthotropic plate, with all edges simply supported, subjected to compression on its ends and a known compression or tension on its sides;(b) the same as (a) but with the ends clamped and sides simply supported;(c) a rectangular orthotropic plate, with the ends simply supported and sides clamped, subjected to compression on its ends; and(d) the same as (c) but with all edges clamped.In each case it is shown that the variables involved can all be combined into such a non-dimensional form that a single curve serves to give the value of the end compression required to cause buckling. This curve is identical with the curve of buckling stress coefficient against side ratio for a corresponding isotropic plate under uni-axial compression.

scholarly journals Simulation and Experimental Substantiation of Beam Deflection under Guided End Conditions

2020 ◽  
Vol 9 (2) ◽  
pp. 1782-1791
Keyword(s):  
Point Load ◽  
Beam Deflection ◽  
Loading Conditions ◽  
Test Results ◽  
Physical Test ◽  
Simply Supported ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
End Conditions ◽  
Loading Fixture

This paper studies the nonlinear deflection characteristics of a rectangular cross sectional beam with guided support conditions. In this study two different end conditions namely guided – guided and guided – simply supported have been examined. Beams made with two dissimilar materials for instance, aluminum and steel have been considered for this study. Different loading conditions namely point load and the amalgamation of uniformly distributed load and point load have been taken into account in this study. The nonlinear response of a beam under static loading condition is influenced by various parameters like sectional properties of the beam, material, loading and boundary conditions etc. A separate loading fixture was fabricated using steel to apply the load (Point load and uniformly distributed load). The loading fixture was validated by performing an experimental measurement of the deflection under various loading conditions on a simply supported beam. The corresponding theoretical displacement values were calculated using the findings in literature and compared with test results .Both the results were found matching with each other with an average variation of just 10%. Based on this validation lesson, the loading fixture was incorporated in the actual study. Displacement values from the nonlinear static analysis were predicted using Finite Element Method and correlation was made with the experimental values for the actual beam setup. Close correlation among the numerical and physical test results was achieved and the maximum error was 8%.

Atomic Simulation of the Bending Deformation of a Single-Crystal Simply Supported Nano-Beam

2009 ◽  
Vol 79-82 ◽  
pp. 1185-1188 ◽  
Author(s):  
Wen Bin Ni ◽  
Jian Wei Zhao ◽  
Yun Hong Liu ◽  
Feng Ying Wang ◽  
Xing Yin
Keyword(s):  
Mechanical Properties ◽  
Single Crystal ◽  
Deformation Behavior ◽  
Surface Effect ◽  
Dynamics Simulation ◽  
Nanoelectromechanical Systems ◽  
Atomic Simulation ◽  
Simply Supported ◽  
Distributed Load ◽  
Uniformly Distributed Load

Advanced fabrication techniques to miniaturize electromechanical systems have brought us into the regime of nanoelectromechanical systems (NEMS). Understanding the mechanical properties of NEMS components is of fundamental importance in the operation of these devices. In this paper, we have reported the deformation behavior of a single-crystal simply supported nano-beam under the uniformly distributed load. By using the molecular dynamics simulation, we have investigated the influence of span the nano-beam on the bending characters. Due to surface effect, the nano-beam shows a different behavior under the uniformly distributed load.

scholarly journals Mathematical model of a moment-less arch

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160019 ◽  
Author(s):  
W. J. Lewis
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Constant Cross Section ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Geometrical Shapes ◽  
Parabolic Form ◽  
The Moment ◽  
Arch Forms

This paper presents a mathematical model for predicting the geometrical shapes of rigid, two-pin, moment-less arches of constant cross section. The advancement of this work lies in the inclusion of arch self-weight and the ability to produce moment-less arch forms for any span/rise ratio, and any ratio of uniformly distributed load per unit span, w , to uniformly distributed arch weight per unit arch length, q . The model is used to derive the shapes of two classical ‘moment-less’ arch forms: parabolic and catenary, prior to demonstrating a general case, not restricted by the unrealistic load assumptions (absence of q , in the case of a parabolic form, or no w , in the case of a catenary arch). Using the same value of span/rise ratio, and w / q >1, the behaviour of the moment-less and parabolic arches under permanent loading, ( w + q ), is analysed. Results show the former to be developing much lower stresses than its parabolic rival, even when there are relatively small differences in the two geometries; for a medium span/rise ratio of 4 and w / q =2, differences in the parabolic and moment-less arch geometries would, in practical terms, be viewed as insignificant, but the stresses in them are different.

Under Uniformly Distributed Load are Fixed on one Side (Simple) on the Edge Simply Supported and Fixed Half Bending of Rectangular Plates

2012 ◽  
Vol 152-154 ◽  
pp. 840-845
Author(s):  
Ying Jie Chen ◽  
Bao Lian Fu ◽  
Liang Wang ◽  
Jie Wu
Keyword(s):  
Rectangular Plate ◽  
Variable Method ◽  
Engineering Practice ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Surface Deflection ◽  
Mixed Variable

In this paper mixed variable method is generalized to solve the problem of bending of the rectangular plate with one side is fixed (simple) on the edge simply supported and fixed half under the action of a uniformly distributed load. Gives the surface deflection equation and a chart, the chart can be directly applied to engineering practice.

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