An analytical solution of three-dimensional steady thermodynamic analysis for a piezoelectric laminated plate using refined plate theory

2017 ◽  
Vol 162 ◽  
pp. 194-209 ◽  
Author(s):  
Hao-Jie Jiang ◽  
Li-Hua Liang ◽  
Li Ma ◽  
Jing Guo ◽  
Hong-Liang Dai ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Thermodynamic Analysis ◽  
Plate Theory ◽  
Three Dimensional ◽  
Laminated Plate ◽  
Refined Plate Theory

A Study of Transverse Shrinkage and Vertical Displacement in Induction Triangle Heating

2012 ◽  
Vol 566 ◽  
pp. 82-87
Author(s):  
Truong Thinh Nguyen
Keyword(s):  
Analytical Solution ◽  
Steel Plate ◽  
Plate Theory ◽  
Plastic Region ◽  
Vertical Displacement ◽  
Heating Process ◽  
Laminated Plate ◽  
Magnetic Analysis ◽  
Electro Magnetic ◽  
Transverse Shrinkage

Deformations including transverse shrinkage and vertical displacement of induction triangle heating play an important role in shipyard. However, the deformations and behaviors of plate after heating are complex, the analysis of this process consumes much time and expensive. The objective of this paper was to develop an analytical solution to determine transverse shrinkage and vertical displacement in induction triangle heating based on laminated plate theory. The plastic region in the analytical solution of the angular deformation and shrinkage of a steel plate is obtained from the thermal analysis of the plate with the heat input calculated from the electro-magnetic analysis of the induction heating process. Calculated values obtained with analytical solution correspond closely to the experimental results.

Elasticity Theory of Plates and a Refined Theory

1979 ◽  
Vol 46 (3) ◽  
pp. 644-650 ◽  
Author(s):  
Shun Cheng
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Three Dimensional ◽  
Fundamental Equation ◽  
Present Theory ◽  
Refined Theory ◽  
Refined Plate Theory ◽  
Elasticity Equations ◽  
Theory Of Plates ◽  
Fundamental Equations

A method for the solution of three-dimensional elasticity equations is presented and is applied to the problem of thick plates. Through this method three governing differential equations, the well-known biharmonic equation, a shear equation and a third governing equation, are deduced directly and systematically from Navier’s equations. It is then shown that the solution of the second fundamental equation (the shear equation) is in fact related to the shear deformation in the bending of plates, hence it may be appropriately called the shear solution and the equation the shear equation. Moreover, it is found that the solution of the third fundamental equation does not yield transverse shearing forces. Because of these results, a refined plate theory which takes into account the transverse shear deformation can now be explicitly established without employing assumptions. With the present theory three boundary conditions at each edge of the plate and all the fundamental equations of elasticity can be satisfied. As an illustrative example, the present theory is applied to the problem of torsion resulting in exactly the same solution as the Saint Venant’s solution of torsion, although the two approaches are appreciably different. The second example also illustrates that accurate solutions, as compared with exact solutions, can be obtained by means of the refined plate theory.

Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates

1999 ◽  
Vol 67 (3) ◽  
pp. 558-567 ◽  
Author(s):  
S. S. Vel ◽  
R. C. Batra
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Laminated Plates ◽  
The Body ◽  
Rectangular Plates ◽  
Laminated Plate ◽  
Various Boundary Conditions ◽  
Linear Piezoelectricity ◽  
Piezoelectric Plates

Analytical solutions for the static three-dimensional deformations of multilayered piezoelectric rectangular plates are obtained by using the Eshelby-Stroh formalism. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thicknesses. The equations of static, linear, piezoelectricity are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series; the continuity conditions at the interfaces and boundary conditions at the edges are used to determine the coefficients. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. Results are presented for thick piezoelectric plates with two opposite edges simply supported and the other two subjected to various boundary conditions. [S0021-8936(00)01803-1]

Refined plate theory and its variants

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 137-146 ◽  
Author(s):  
R. P. Shimpi
Keyword(s):  
Plate Theory ◽  
Refined Plate Theory
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