Bending Solutions of Sectorial Thick Plates Based on Reissner Plate Theory

2005 ◽  
Vol 33 (1) ◽  
pp. 51-77 ◽  
Author(s):  
C.M. Wang ◽  
I.M. Nazmul ◽  
T. Matsumoto ◽  
Q. Wang
Keyword(s):  
Plate Theory ◽  
Thick Plates ◽  
Reissner Plate

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

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.

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 sectorial element based on Reissner plate theory

2000 ◽  
Vol 9 (6) ◽  
pp. 519-540 ◽  
Author(s):  
A. Yalcin Akoz ◽  
Nihal Eratli
Keyword(s):  
Plate Theory ◽  
Reissner Plate

A Mindlin–Reissner Variational Principle to Analyze the Behavior of Moderately Thick Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S32-S38
Author(s):  
Roberto S. Carnicer ◽  
Stefano Alliney
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Plate Theory ◽  
Mindlin Plate ◽  
General Boundary Conditions ◽  
Thick Plates ◽  
Numerical Examples ◽  
Simple Support ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates

In the present work a method to solve the plate behavior under the assumption of the Mindlin plate theory is analyzed by means of finite element techniques, avoiding the tendency of the thin element to lock when the thickness of the plates becomes very small. A different formulation is developed from the Mindlin–Reissner principle for general boundary conditions. Numerical examples to evaluate the noninfluence of locking on clamped and simple support plates are calculated.

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