The Refined Theory of One-Dimensional Quasi-Crystals in Thick Plate Structures

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Yang Gao ◽  
Andreas Ricoeur
Keyword(s):  
Thick Plate ◽  
Ad Hoc ◽  
Plate Theory ◽  
Pure Shear ◽  
Refined Theory ◽  
Plate Structures ◽  
Thick Plates ◽  
Refined Plate Theory ◽  
One Dimensional ◽  
Quasi Crystals

For one-dimensional quasi-crystals, the refined theory of thick plates is explicitly established from the general solution of quasi-crystals and the Luré method without employing ad hoc stress or deformation assumptions. For a homogeneous plate, the exact equations and solutions are derived, which consist of three parts: the biharmonic part, the shear part, and the transcendental part. For a nonhomogeneous plate, the exact governing differential equations and solutions under pure normal loadings and pure shear loadings, respectively, are obtained directly from the refined plate theory. In an illustrative example, explicit expressions of analytical solutions are obtained for torsion of a rectangular quasi-crystal plate.

The Refined Theory of Plane Problems for One-Dimensional Quasicrystalline Bodies

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Yang Gao ◽  
Andreas Ricoeur
Keyword(s):  
Ad Hoc ◽  
Three Dimensional ◽  
Refined Theory ◽  
Shear Surface ◽  
Surface Loading ◽  
Thick Plates ◽  
One Dimensional ◽  
Nonhomogeneous Boundary ◽  
Deformation Regime ◽  
Nonhomogeneous Boundary Conditions

Without employing ad hoc assumptions, various equations and solutions for plane problems of one-dimensional quasicrystals are deduced systematically. A method for the exact solution of three-dimensional equations is presented under homogeneous and nonhomogeneous boundary conditions. The equations and solutions are used to construct the refined theory of thick plates for both an in-plane extensional deformation regime and a normal or shear surface loading. With this method, the refined theory can now be explicitly established from the general solution of quasicrystals and the Lur’e method. In two illustrative examples of infinite plates with a circular hole, it is shown that explicit expressions of analytical solutions can be obtained by using the refined theory.

The Refined Theory of Axisymmetric Circular Cylinder in One-Dimensional Hexagonal Quasicrystals

2012 ◽  
Vol 217-219 ◽  
pp. 1421-1424 ◽  
Author(s):  
Bao Sheng Zhao ◽  
Di Wu
Keyword(s):  
General Solution ◽  
Circular Cylinder ◽  
Ad Hoc ◽  
Approximate Equation ◽  
Refined Theory ◽  
One Dimensional ◽  
Stress Components ◽  
Refined Equation ◽  
Independent Variable ◽  
1D Hexagonal Quasicrystals

A refined theory of axisymmetric cylinder in one-dimensional (1D) hexagonal quasicrystals (QCs) is analyzed. Based on elastic theory with 1D hexagonal QCs, the refined theory of axisymmetric cylinder is derived by using general solution of 1D hexagonal QCs and Lur’e method without ad hoc assumptions. At first, expressions were obtained for all the phonon and phason displacements and stress components in term of the three functions with single independent variable. Based on the boundary conditions, the refined equation for the cylinder is derived directly. And the approximate equation is accurate up to the second-order terms with respect to radius of circular cylinder.

Locating Impact on Thick Plates by Acoustic Wave Analysis

2008 ◽  
Author(s):  
Ho-Wuk Kim ◽  
Sang-Kwon Lee
Keyword(s):  
Power Plant ◽  
Nuclear Power Plant ◽  
Group Velocity ◽  
Steam Generator ◽  
Nuclear Power ◽  
Thick Plate ◽  
Impact Load ◽  
Plate Theory ◽  
Thick Plates ◽  
The Impact

Loose parts in a steam generator of a nuclear power plant often impact the wall of the generator and become one of the damage sources in the nuclear power plant. In general, the steam generator of the nuclear power plant is structured by thick plates. This paper presents a novel approach to locating an impact load in a thick plate. The approach is based on an analysis of the acoustic waveforms measured by a sensor array located on the plate surface and theoretically obtained by either the exact elastodynamic or theory the approximate shear deformation plate theory (SDPT). For accurate estimation of the location of the impact source due to loose part, the time differences in the arrival times of the waves at the sensors and their propagation velocities are determined. This is accomplished through the use of a combined higher order time frequency (CHOTF) method, which is capable of detecting signals with lower signal to noise ratio compared to other available methods. The dispersion curves for multi modes of Lamb waves are calculated by using exact plate theory and SDPT. It is difficult to measure directly the group velocity for Lamb mode of acoustic waveform in the thick plate because they are dispersive waves. However, most of the energy in the wave is carried by the flexural waves (A0 mode); the group velocity of this mode is extracted by using the CHOTF technique for estimating the impact source location. The estimates are shown to be in excellent agreement with the actual locations and the technique is applied to the detection of the location of the impact load due to the loose part in a nuclear power plant.

A Refined Theory of Moderately Thick Plates According to Exposition of the Classical Technical Theories, Theoretical Aspects

2014 ◽  
Vol 578-579 ◽  
pp. 822-829
Author(s):  
Jose Miguel Martinez Valle
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Middle Surface ◽  
Second Order ◽  
Refined Theory ◽  
Order Of Accuracy ◽  
Thick Plates ◽  
Shear Deformation Plate Theory ◽  
Moderately Thick Plates

In this paper we propose a new refined shear deformation plate theory. This theory possesses a series of desirable features, the most salient of which areas follows: (i) The loads, which are usually considered to be applied on the middle surface of the plate, are applied in this new theory on the top surface of the plate; (ii) The equations deduced provide the same order of accuracy as several theories with second order shear deformation effects; (iii) It constitutes a theory, in the sense defined by Love, since it gives easy expressions for application to problems in different fields in architecture and engineering.

scholarly journals Flexure of Thick Plates Resting on Elastic Foundation Using Two-Variable Refined Plate Theory

2015 ◽  
Vol 62 (2) ◽  
pp. 181-203 ◽  
Author(s):  
Jafar Rouzegar ◽  
Reza Abdoli Sharifpoor
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Plate Thickness ◽  
Benchmark Problems ◽  
Shear Stresses ◽  
Rectangular Plates ◽  
Governing Equations ◽  
Thick Plates ◽  
Refined Plate Theory ◽  
Winkler Elastic Foundation

Abstract The two-variable refined plate theory is used in this paper for the analysis of thick plates resting on elastic foundation. This theory contains only two unknown parameters and predicts parabolic variation of transverse shear stresses. It satisfies the zero traction on the plate surfaces without using shear correction factor. Using the principle of minimum potential energy, the governing equations for simply supported rectangular plates resting on Winkler elastic foundation are obtained. The Navier method is adopted for solution of obtained coupled governing equations, and several benchmark problems under various loading conditions are solved by present theory. The comparison of obtained results with other common theories shows the excellent efficiency of this theory in modeling thick plates resting on elastic foundation. Also, the effect of foundation modulus, plate thickness and type of loading are studied and the results show that the deflections are decreased by increasing the foundation modulus and plate thickness

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.

Random Response of Thick Laminated Rectangular Plates

1991 ◽  
Vol 113 (3) ◽  
pp. 286-291 ◽  
Author(s):  
R. S. Srinivasan ◽  
P. A. Krishnan
Keyword(s):  
Plate Theory ◽  
Order Theory ◽  
Response Analysis ◽  
Refined Theory ◽  
Rectangular Plates ◽  
Random Response ◽  
Refined Plate Theory ◽  
First Order ◽  
White Noise Excitation ◽  
First Order Theory

The present paper deals with the random response analysis of clamped thick laminated rectangular plates subjected to white noise excitation. The refined plate theory postulated by Reddy has been used. The analysis has been done using an integral equation technique. The random response results obtained for istropic square plates based on different plate theories (viz.) classical theory, first order theory and refined theory, have been compared. A parametric study has been conducted for angle ply and cross ply plates by varying the lay up of layers and a/h ratios.

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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