Higher-order piezoelectric plate theory derived from a three-dimensional variational principle

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 91-104 ◽  
Author(s):  
R. C. Batra ◽  
S. Vidoli
Keyword(s):  
Variational Principle ◽  
Piezoelectric Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

The analysis of inter-laminar stress and electric potential for a laminated piezoelectric plate with interfacial damage

2011 ◽  
Vol 16 (8) ◽  
pp. 793-811 ◽  
Author(s):  
Fu Yiming ◽  
Li Sheng
Keyword(s):  
Electric Potential ◽  
Degrees Of Freedom ◽  
Piezoelectric Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Variation Principle ◽  
Interfacial Damage ◽  
Load Models ◽  
Non Linear ◽  
Piezoelectric Plates

This paper presents a non-linear model for laminated piezoelectric plates with inter-laminar mechanical and electrical damage. The model is based on the general six-degrees-of-freedom plate theory, and the discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the variation principle, the three-dimensional non-linear equilibrium differential equations of simply supported laminated piezoelectric plates with interfacial damage are derived. Then, an analytical solution is presented by using the finite difference method. In numerical examples, the effects of different damage values, load models, and electric boundary conditions on the inter-laminar stress and electric potential profile of a laminated piezoelectric plate with interfacial imperfections are investigated.

Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory

2008 ◽  
Vol 222 (8) ◽  
pp. 1443-1452 ◽  
Author(s):  
M K Pandit ◽  
A H Sheikh ◽  
B N Singh
Keyword(s):  
Transverse Shear ◽  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Thickness Variation ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Zigzag Theory ◽  
Three Dimensional Elasticity

This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.

The Interlaminar Stresses Analysis of Composite Laminated Plates Based on the Generalized Higher-Order Global-Local Plate Theory

2013 ◽  
Vol 785-786 ◽  
pp. 239-243
Author(s):  
Wei Dong Chen ◽  
Ping Jia ◽  
Jian Cao Li ◽  
Feng Chao Zhang ◽  
Yan Chun Yu ◽  
...  
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Fortran Program ◽  
Laminated Plates ◽  
Local Theory ◽  
Shear Stresses ◽  
Interlaminar Stresses ◽  
Integration Problem ◽  
Triangular Area

A generalized higher-order global-local theory was presented. The transverse shear stresses can be got directly through the constitutive equation without using the equilibrium equation. The second derivative of interpolation function was deduced. The hammer integration of triangular area coordinate method was applied to solve the multiple integration problem of the element stiffness matrix. The order choice of numerical integration was discussed and results obtained through two different integration orders were compared. The flow of how to compile a FORTRAN program was given. A moderately thick composite laminated plate was analyzed via finite element method (FEM) based on the theory and results were compared with that of Paganos three-dimensional elasticity. It shows that the interlaminar stresses are accurate for moderately thick laminated plates.

VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

2001 ◽  
Vol 09 (04) ◽  
pp. 1259-1286 ◽  
Author(s):  
MIGUEL R. VISBAL ◽  
DATTA V. GAITONDE
Keyword(s):  
Three Dimensional ◽  
Radiation Condition ◽  
Higher Order ◽  
High Order ◽  
High Frequencies ◽  
Decomposition Strategies ◽  
The Impact ◽  
Spurious Modes ◽  
Very High ◽  
Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

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