Static Analysis of a Laminated Beam

1973 ◽  
Vol 95 (3) ◽  
pp. 755-761 ◽  
Author(s):  
R. A. DiTaranto
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Static Analysis ◽  
Middle Layer ◽  
Uniform Load ◽  
Rigid Boundary ◽  
Maximum Displacement ◽  
Laminated Beam ◽  
Geometrical Properties ◽  
Governing Differential Equation

The governing differential equation and natural and rigid boundary conditions have been obtained for a three-layer beam having a middle layer which is primarily shear carrying, using a variational method. Results have been obtained for a fixed-fixed and symply supported beam having a uniform load. For beams having these boundary and loading conditions, curves are presented showing the effect of varying the physical and geometrical properties of the laminated beam on the maximum displacement and stress.

scholarly journals Static Analysis of the Effect of Shape Memory Alloy in Laminated Beam

2021 ◽  
Vol 12 (2) ◽  
pp. 2114-2124
Author(s):  
Radha Tomar, Et. al.
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Static Analysis ◽  
Middle Layer ◽  
Static Response ◽  
Laminated Beam ◽  
The Third ◽  
First Case ◽  
Cantilevered Beam ◽  
Ansys Workbench

This study deals with the effect of shape memory alloy in carbon/epoxy laminated beam. In this study we analyses static response of laminated beam under the load of 10 KN at the mid span of the beam. In this study a cantilevered beam of dimension 1000mm length, 100mm width and 30mm height which is divided in 3 layers of 10mm each is considered. The study includes three cases. In first case all the 3 layers of beam is laminated with carbon/epoxy. In second case the top and the bottom layers are laminated with carbon/epoxy and middle layer is2qw laminated with shape memory alloy. In the third case the top and the bottom layers are laminated with shape memory alloy while the middle with carbon/epoxy. Loading and boundary conditions are same for all the three cases. All the analysis is done using ANSYS workbench 15.0

On linear wave motions in magnetic-velocity shears

1977 ◽  
Vol 285 (1328) ◽  
pp. 607-636 ◽  
Keyword(s):  
Differential Equation ◽  
Critical Level ◽  
Velocity Shear ◽  
Linear Wave ◽  
Wave Amplification ◽  
Isothermal Fluid ◽  
Governing Differential Equation ◽  
Boussinesq Fluid ◽  
Propagation Properties ◽  
Background State

The propagation properties of linear wave motions in magnetic and/or velocity shears which vary in one coordinate z (say) are usually governed by a second order linear ordinary differential equation in the independent variable z. It is proved that associated with any such differential equation there always exists a quantity A which is independent of z. By employing A a measure of the intensity of the wave, this result is used to investigate the general propagation properties of hydromagnetic-gravity waves (e.g. critical level absorption, valve effects and wave amplification) in magnetic and/or velocity shears, using a full wave treatment. When variations in the basic state are included, the governing differential equation usually has more singularities than it has in the W.K.B.J. approximation, which neglects all variations in the background state. The study of a wide variety of models shows that critical level behaviour occurs only at the singularities predicted by the W.K.B.J. approximation. Although the solutions of the differential equation are necessarily singular at the irregularities whose presence is solely due to the inclusion of variations in the basic state, the intensity of the wave (as measured by A) is continuous there. Also the valve effect is found to persist whatever the relation between the wavelength of the wave and the scale of variations of the background state. In addition, it is shown that a hydromagnetic-gravity wave incident upon a finite magnetic and/or velocity shear can be amplified (or over-reflected) in the absence of any critical levels within the shear layer. In a Boussinesq fluid rotating uniformly about the vertical, wave amplification can occur if the horizontal vertically sheared flow and magnetic field are perpendicular. In a compressible isothermal fluid, on the other hand, wave amplification not only occurs in both magnetic-velocity and velocity shears but also in a magnetic shear acting alone.

scholarly journals New Bi-modular Material Approach to Buckling Problem of Reinforced Concrete Columns

2016 ◽  
Vol 6 (1) ◽  
pp. 19 ◽  
Author(s):  
Ahmad Salah Edeen Nassef ◽  
Mohammed A. Dahim
Keyword(s):  
Differential Equation ◽  
Reinforced Concrete ◽  
Differential Equations ◽  
Concrete Columns ◽  
Neutral Axis ◽  
Reinforced Concrete Columns ◽  
New Approach ◽  
Codes Of Practice ◽  
Governing Differential Equation ◽  
Transverse Deflection

<p class="1Body">This paper was investigating the buckling problem of reinforced concrete columns considering the reinforced concrete as bi – modular material. Governing differential equations was driven. The relation between the non-dimensional transverse deflection and non-dimensional distance between centroid axis and the neutral axis "eccentricity" was drawn to enable the solution of the governing differential equation. The new approach was verified with different experimental results and different codes of practice.<strong></strong></p>

Analysis of Mechanophysical Properties of Fritillaria ussuriensis Maxim and Designing of Grade Sieve Machine

2013 ◽  
Vol 764 ◽  
pp. 165-168
Author(s):  
Jiang Song ◽  
Song Zhuo Lu ◽  
Li Hua Liu ◽  
Ming Wang ◽  
Tian Xiang Liu
Keyword(s):  
Mechanical Properties ◽  
Friction Coefficient ◽  
Physical And Mechanical Properties ◽  
Middle Layer ◽  
Mathematical Statistics ◽  
Angle Of Repose ◽  
Screening Process ◽  
Geometrical Properties ◽  
Pore Dimension ◽  
Main Index

Based on the field and lab measuerement in harvest time, Physical and mechanical properties of fritillaria ussuriensis maxim (FUM) are researched. Geometrical properties of FUM are analyzed using mathematical statistics method, and the variation sections of main index values of two kinds of FUM are obtained. Mechanical properties of FUM outsifting in screen penetrating process are tested by means of friction experiment, the friction coefficient and angle of repose of two kinds of FUM are obtained using mathematical statistics method. Grade sieve machine is designed based on the analysis of mechanophysical properties of FUM. The main parameters are: shape of sieve pore is rectangle, screen diameter is 20mm, sieve pore dimension of upper layer is 13×20mm2, middle layer is 9×18mm2, and under layer is 7×10mm2. By testing of friction coefficient and angle of repose and movement and dynamics analysis of grade sieve, outsifting velocity is 7<<9rad/s and acceleration is 4<a<13m/s2 in screening process.

scholarly journals An Analytical Study of Weakly Nonlinear Dynamics of a Walters’ Liquid B around a Flexible Sheet Undergoing Super Linear Stretching

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
P. G. Siddheshwar ◽  
A. Chan ◽  
U. S. Mahabaleswar
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equation ◽  
Boundary Layer ◽  
Analytical Study ◽  
Stretching Sheet ◽  
Quadratic Function ◽  
Weakly Nonlinear ◽  
Governing Differential Equation ◽  
Layer Flow ◽  
Analytical Expressions

The paper discusses the boundary layer flow of Walters’ liquid B over a stretching sheet. The stretching is assumed to be a quadratic function of the coordinate along the direction of stretching. The study encompasses within its realm both Walters’ liquid B and second order liquid. The velocity distribution is obtained by solving the nonlinear governing differential equation. Analytical expressions are obtained for stream function and velocity components as functions of the viscoelastic and stretching related parameters. It is shown that the viscoelasticity goes hand in hand with quadratic stretching in enhancing the lifting of the liquid as we go along the sheet.

scholarly journals On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Luciano Feo ◽  
Rosa Penna
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Scale Parameter ◽  
Elastic Equilibrium ◽  
Functionally Graded ◽  
Constitutive Law ◽  
Bending Moments ◽  
Innovative Methodology ◽  
Governing Differential Equation ◽  
Nonlocality Effect

Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic is integrated in terms of transverse displacements and equilibrated bending moments. Benchmark examples are developed, thus providing the nonlocality effect in nanocantilever and clampled-simply supported nanobeams for selected values of the Eringen scale parameter.

Rotating Disk Shape: Is the Equation Nonlinear?

1989 ◽  
Vol 111 (4) ◽  
pp. 456-458
Author(s):  
R. R. Jettappa
Keyword(s):  
Differential Equation ◽  
Linear Equation ◽  
Rotating Disk ◽  
Variable Coefficients ◽  
Thin Disk ◽  
Second Order ◽  
First Order ◽  
Governing Differential Equation ◽  
Centrifugal Loading

The determination of the shape of a rotating disk under centrifugal loading is considered. It is shown that the governing differential equation for the shape of a rotating thin disk is reducible to a linear equation of second order with variable coefficients. However, the form of this equation is such that it can be treated as an equation of first order thereby facilitating the integration by quadratures. All this is possible without any additional mathematical assumptions so that the results are exact within the limitations of the thin disk theory.

scholarly journals An investigation into the effects of heat transfer on the motion of a spherical bubble

2004 ◽  
Vol 45 (3) ◽  
pp. 361-371 ◽  
Author(s):  
P. J. Harris ◽  
H. Al-Awadi ◽  
W. K. Soh
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Results ◽  
Transfer Effects ◽  
Rigid Boundary ◽  
Spherical Bubble ◽  
Heat Transfer Effects ◽  
Surrounding Fluid

AbstractThis paper investigates the effect of heat transfer on the motion of a spherical bubble in the vicinity of a rigid boundary. The effects of heat transfer between the bubble and the surrounding fluid, and the resulting loss of energy from the bubble, can be incorporated into the simple spherical bubble model with the addition of a single extra ordinary differential equation. The numerical results show that for a bubble close to an infiniterigid boundary there are significant differences in both the radius and Kelvin impulse of the bubble when the heat transfer effects are included.

Dimensional Analysis in Design

1988 ◽  
Vol 110 (3) ◽  
pp. 401-407 ◽  
Author(s):  
J. R. Schnittger
Keyword(s):  
Differential Equation ◽  
Dimensional Analysis ◽  
Journal Bearing ◽  
Mechanical Design ◽  
Turbine Blades ◽  
Helical Spring ◽  
Disk Brake ◽  
Governing Differential Equation ◽  
Bearing Vibration ◽  
New Guidelines

New guidelines for dimensional analysis remove traditional road-blocks to its widespread use in mechanical design. Cases, with or without prior formula given, are exposed as well as those with a governing differential equation. The examples include bevel gear, helical spring, centrifugal pump, journal bearing, vibration of turbine blades, and a disk brake. A matrix method to determine nondimensional groups is reviewed.

Sign in / Sign up

Export Citation Format

Share Document