Three-dimensional elasticity solution for laminated cross-ply panel under localized moment

2007 ◽  
Vol 221 (8) ◽  
pp. 859-866
Author(s):  
A Alibeigloo ◽  
M Shakeri
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Three Dimensional ◽  
Axial Direction ◽  
Variable Coefficients ◽  
Cylindrical Panel ◽  
Fourier Series Expansion ◽  
Simply Supported ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solutions have been presented for thick laminated crossply circular cylindrical panel. The panel is under localized patch moment in axial direction and is simply supported at all edges with finite length. Ordinary differential equations with variable coefficients are obtained by means of Fourier series expansion for displacement field and loading in the circumferential and axial directions. Resulting ordinary differential equations are solved using Taylor series. Numerical results are presented for (0/90°) and (0/90/0°) lay-up, and compared with the results for simple form of loading published in literatures.

Elasticity solution for thick laminated anisotropic cylindrical panels under dynamic load

2002 ◽  
Vol 216 (3) ◽  
pp. 315-322 ◽  
Author(s):  
A Alibiglu ◽  
M Shakeri ◽  
M R Eslami
Keyword(s):  
Differential Equations ◽  
Dynamic Load ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Cylindrical Panel ◽  
Great Length ◽  
Elasticity Equations ◽  
Shell Panel ◽  
Asymmetric Load ◽  
Three Dimensional Elasticity

The dynamic response of an axisymmetric arbitrary laminated anisotropic cylindrical panel subjected to asymmetric load is studied on the basis of three-dimensional elasticity equations. The shell panel has a great length and is simply supported at both edges. The highly coupled partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) with variable coefficients by means of trigonometric function expansion in circumferential directions. The resulting OPEs are solved by Galerkin's finite element method. Numerical examples are presented for 45°/-45° and 45°/-45°/45° laminations under dynamic load. Finally, the results are compared with published results.

Dynamic analysis of functionally graded plate integrated with two piezoelectric layers, based on a three-dimensional elasticity solution

2009 ◽  
Vol 223 (6) ◽  
pp. 1297-1309 ◽  
Author(s):  
M Shakeri ◽  
S N Sadeghi ◽  
M Javanbakht ◽  
H Hatamikian
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Series Expansion ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates ◽  
Piezoelectric Layers ◽  
Three Dimensional Elasticity

In this article, dynamic analysis of functionally graded (FG) plates integrated with two piezoelectric layers has been carried out. The rectangular plate is simply supported at four edges and exposed to dynamic excitation. Three-dimensional elasticity equations have been considered. Using a series expansion of mechanical and electrical displacements, the partial differential equations have been reduced to ordinary differential equations (ODEs) with variable coefficients. The solution of the resulting system of ODEs has been carried out using the Galerkin method. The final result is obtained by taking just one term in the series expansion. The Newmark method has been used to move forward in the time domain for a dynamic solution. Finally, numerical results have been presented for a simply supported rectangular FG plate integrated with two piezoelectric layers. In some cases, results have been compared to previously published works.

Vibration Characteristics of Simply Supported Thick Skew Plates in Three-Dimensional Setting

1995 ◽  
Vol 62 (4) ◽  
pp. 880-886 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Elasticity Theory ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Skew Angle ◽  
Simply Supported ◽  
Significant Difference ◽  
Simple Support ◽  
Elasticity Solutions ◽  
Support Conditions ◽  
Three Dimensional Elasticity

A procedure is presented for determining the three-dimensional elasticity solutions for free vibration analysis of simply supported thick skew plates. The exact expressions of strain and kinetic energies are derived from linear, small-strain, three-dimensional elasticity theory. To allow the treatment of soft and hard simple support conditions, sets of three-dimensional spatial displacement functions are expressed in terms of unit normals to the edges. By virtue of the three-dimensional elasticity theory, the present method does not require a special treatment for stress singularity at the obtuse corners. This method is also demonstrated to be free from shear locking phenomena. The significant difference in the vibration response of skew plates with soft and hard simple support conditions is highlighted. The influence of skew angle on the eigenvalues of thick skew plate is discussed in the context of the three-dimensional elasticity solutions.

Dynamic Thermal Analysis of Laminated Cylinder with a Piezoelectric Layer Based on Three-Dimensional Elasticity Solution

2012 ◽  
Vol 186 ◽  
pp. 16-25
Author(s):  
A.R. Daneshmehr ◽  
S. Akbari ◽  
A. Nateghi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Piezoelectric Layer ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Elasticity Solution ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solution is presented for finite length, simply supported, laminated cylinder with a piezoelectric layer under dynamic thermal load and pressure. The piezoelectric layer can be used as an actuator or a sensor. The ordinary differential equations are obtained from partial differential equations of motion by means of trigonometric function expansion in longitudinal direction. Galerkin finite element method is used to solve the resulting ordinary differential equations. Finally numerical results are discussed for different situations.

Elasticity Solutions for Laminated Orthotropic Cylindrical Shells Subjected to Localized Longitudinal and Circumferential Moments

2003 ◽  
Vol 125 (1) ◽  
pp. 26-35 ◽  
Author(s):  
K. Bhaskar ◽  
N. Ganapathysaran
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Laminated Composite ◽  
Two Dimensional ◽  
Simply Supported ◽  
Elasticity Solutions ◽  
Laminated Composite Shells ◽  
Taylor’S Series

The purpose of this work is to present baseline elasticity solutions for laminated composite shells subjected to localized moments. For simply supported cross-ply cylindrical shells, the problem reduces to one of coupled ordinary differential equations which are solved in terms of Taylor’s series. Results, in the form of tables and graphs, are presented for the cases of longitudinal and circumferential moments. These results would be very useful for judging the accuracy of approximate two-dimensional shell theories. They are used herein to study the errors of a shell theory based on the classical Love-Kirchhoff hypothesis.

Three-Dimensional Elasticity Study of Vibration of a Composite Shell Panel with Embedded Piezoelectric Sensors

2012 ◽  
Vol 186 ◽  
pp. 87-97
Author(s):  
Alireza R. Daneshmehr ◽  
Samaun Nili ◽  
A.R. Nateghi ◽  
Shirjan Hussaini
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Natural Frequencies ◽  
Composite Shell ◽  
Three Dimensional ◽  
Trigonometric Function ◽  
Partial Differential ◽  
Shell Panel ◽  
Three Dimensional Elasticity

In this paper, Free vibration analysis of a finite length composite shell panel with an embedded piezoelectric sensor, using three-dimensional elasticity solution, is presented. To this end, two different methods are applied to solve the governing equations of the problem. In the first method, the displacement field is derived using trigonometric function expansion in circumferential and longitudinal directions. Using the method of changing variables, the governing partial differential equations are reduced to ordinary differential equations. Then these equations are solved simultaneously with outer and inner boundary conditions to give the natural frequencies and shape modes of the shell panel. In the second method the highly coupled partial differential equations are reduced to ordinary differential equations by means of trigonometric function expansion in circumferential and axial directions and then the finite difference method is applied to evaluate the obtained differential equations in radial direction. Then, the natural frequencies of the multi-layered panel are calculated using the obtained ordinary differential equations. At last, some numerical examples are presented to compare the results obtained by these two different methods. Three layered laminated shell panel is assumed to be [0/90/P].

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

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