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.

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.

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.

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].

The Invariant Subspace Method for Solving Fractional Partial Differential Equations

2020 ◽  
pp. 267-282
Author(s):  
Mohamed Soror Abdel Latif ◽  
Abass Hassan Abdel Kader
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Balance Principle ◽  
New Exact Solutions

In this chapter, the authors discuss the effectiveness of the invariant subspace method (ISM) for solving fractional partial differential equations. For this purpose, they have chosen a nonlinear time fractional partial differential equation (PDE) with variable coefficients to be investigated through this method. One-, two-, and three-dimensional invariant subspace classifications have been performed for this equation. Some new exact solutions have been obtained using the ISM. Also, the authors give a comparison between this method and the homogeneous balance principle (HBP).

The Response Analysis of the Piezoelectric Shell Panel Actuators Based on the Theory of Elasticity

Volume 2 ◽  
2004 ◽  
Author(s):  
A. Daneshmehr ◽  
M. Shakeri
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Coefficients ◽  
Theory Of Elasticity ◽  
Response Analysis ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Piezoelectric Layers ◽  
Shell Panel ◽  
Piezoelectric Shell

A study on the elasticity solution of shell panel piezoelectric actuators is presented. In this paper, the structure is infinitely long, simply-supported, orthotropic and under pressure and electrostatic excitation. The equations of equilibrium, which are coupled partial differential equations, are reduced to ordinary differential equations with variable coefficients by means of trigonometric function expansion in circumferential direction. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical results are presented for [0/90/P] lamination. Finally the results are compared with the assumption of piezoelectric layers in published results.

Three-Dimensional Analysis of an Elastic Plate-Cylinder Intersection by the Boundary-Point-Least-Squares Technique

1977 ◽  
Vol 99 (1) ◽  
pp. 17-25 ◽  
Author(s):  
D. Redekop
Keyword(s):  
Boundary Conditions ◽  
Least Squares ◽  
Boundary Point ◽  
Shell Theory ◽  
Three Dimensional ◽  
Middle Part ◽  
Elasticity Equations ◽  
Three Dimensional Elasticity ◽  
Tension Loading ◽  
Theoretical Results

The boundary-point-least-squares technique is applied to the axisymmetric three-dimensional elasticity problem of a hollow circular cylinder normally intersecting with a perforated flat plate. The geometry of the intersection is partitioned into three parts. Boundary conditions on the middle part and continuity conditions between adjacent parts are satisfied using the numerical boundary-point-least-squares technique while the governing elasticity equations and all other boundary conditions are satisfied exactly. Sample theoretical results are presented for the case of axisymmetric radial tension loading on the plate. The results compare favorably with previously published experimental data and provide supplementary data to theoretical results obtained using existing shell theory solutions.

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