Derivation of particular solutions for linear loading in the thick plate theory

2000 ◽  
Vol 25 (4) ◽  
pp. 385-393 ◽  
Author(s):  
Y. F. Rashed
Keyword(s):  
Thick Plate ◽  
Plate Theory ◽  
Particular Solutions ◽  
Linear Loading

Analysis of Creep Characteristics of Shallow Mined-Out Areas Roof under Low Stress Conditions

2011 ◽  
Vol 105-107 ◽  
pp. 832-836 ◽  
Author(s):  
Shu Ren Wang ◽  
Hui Hui Jia
Keyword(s):  
Creep Deformation ◽  
Thick Plate ◽  
Plate Theory ◽  
Technical Problem ◽  
Stress Conditions ◽  
Creep Model ◽  
Term Strength ◽  
Creep Characteristics ◽  
Over Time

Under low stress conditions, when the load exerting on the mined-out areas roof is less than the rock long-term strength, the rock roof will generate some creep deformation. In order to prevent the roof of the mined-out areas suddenly collapse, and to ensure the operator and construction equipment above the mined-out areas safety, it is an important security technical problem to reveal the creep characteristics of the shallow mined-out areas roof. Taking the mined-out areas of Antaibao Surface Mine as background, considering the rheological properties of rock roof, and assuming the roof was a rectangular thick plate, the creep characteristics of mined-out areas roof were analysed by applying the thick plate theory and Kelvin creep model. The regression equation of the roof deflection increment over time was given, and the creep characteristics of the shallow mined-out areas roof were revealed also.

scholarly journals Three-dimensional Stress Analysis of a Rectangular Cantilever Plate Using an Extended Love's Moderately Thick Plate Theory

1982 ◽  
Vol 25 (203) ◽  
pp. 720-727
Author(s):  
Michiaki KOBAYASHI ◽  
Toru NAGASAWA ◽  
Hiromasa ISHIKAWA ◽  
Kin-ichi HATA
Keyword(s):  
Stress Analysis ◽  
Thick Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Cantilever Plate ◽  
Moderately Thick Plate

Prediction of Vibration Properties of Sandwich Panel Using Thick Plate Theory

2001 ◽  
Author(s):  
Qunli Liu ◽  
Yi Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Principle ◽  
Free Vibration ◽  
Thick Plate ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Vibration Properties ◽  
Proposed Model ◽  
Thin Plate Theory

Abstract The vibration of a sandwich panel with two identical isotropic facesheets and an orthotropic core was studied. The governing partial differential equation was derived using variational principle. Kirchhoff’s theory was applied to describe the deformation of the panel, and the rotational effect was taken into consideration. The frequencies of free vibration of a rectangular panel can be predicted based on the proposed analytical model. Results based on the proposed model were compared with those from thin plate theory. The effect of orthotropic core on frequencies was also discussed.

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.

ESTIMATION OF IMPACT LOAD IN THICK PLATE BY USING THEORETICAL GREEN FUNCTION AND EXPERIMENTAL MEASUREMENT OF VIBRATION

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1377-1382
Author(s):  
H. W. Kim ◽  
S. K. Lee
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Thick Plate ◽  
Impact Load ◽  
Plate Theory ◽  
Time History ◽  
Force Transducer ◽  
Good Prediction ◽  
History Of ◽  
The Impact

The classic plate theory (CPT) as a theoretical solution to an impact load has been used in a thin plate. However, The CPT is not any more useful solution for the impact load in the industrial power plant, which is generally constructed by the thick plate. In this paper a novel and effective approach is developed to determine the time history of the impact load on a thick aluminum plate based on the analysis of the acoustic waveforms measured by a sensor array located on the thick plate surface in combination with the theoretical Green's function for the plate. The Green's functions are derived based on either the exact elastodynamic or theory the approximate shear deformation plate theory (SDPT). If the displacement is measured on the plate, then the time history of impact load can be calculated by deconvolving the measured displacement with the theoretical Green's function. The reconstructed time history for impact load is compared with the time history of the impact load measured by the force transducer. A good prediction is found. This technique presents a valuable method for identification of source and may be applied to in-service structures under impact to signals recorded from acoustic emission of propagating cracks.

Analysis of Stress Singularities at Bi-Material Corners in Reddy's Theory of Plate Bending

2006 ◽  
Vol 22 (1) ◽  
pp. 67-75 ◽  
Author(s):  
C. S. Huang
Keyword(s):  
Thick Plate ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Stress Singularity ◽  
Numerical Approach ◽  
Sharp Corner ◽  
Equilibrium Equations ◽  
Third Order ◽  
Isotropic Plates ◽  
Expansion Technique

AbstractThe order of stress singularity at a sharp corner of a plate needs to be known before a numerical approach can be taken to determine accurately the stress distribution of a plate with irregular geometry (such as a V-notch) under loading. This work analyzes the order of the stress singularity at a bi-material corner of a thick plate under bending, based on Reddy's third-order shear deformation plate theory. An eigenfunction expansion technique is used to derive the asymptotic displacement field in the vicinity of the sharp corner by solving the equilibrium equations in terms of displacement functions. This paper explicitly shows the first known characteristic equations for determining the order of the stress singularity at the interface corner of a bonded dissimilar isotropic plate. Moreover, the numerical results are given in graphic form for the order of stress singularity at the interface corner in bonded dissimilar isotropic plates and at the vertex of a bi-material wedge with free radial edges. The results presented herein fill some of the gaps in the literature

Failure behavior of hierarchical corrugated sandwich structures with second-order core based on Mindlin plate theory

2017 ◽  
Vol 21 (2) ◽  
pp. 552-579 ◽  
Author(s):  
Gang Li ◽  
Zhaokai Li ◽  
Peng Hao ◽  
Yutian Wang ◽  
Yaochu Fang
Keyword(s):  
Thick Plate ◽  
Failure Modes ◽  
Sandwich Structures ◽  
Plate Theory ◽  
Second Order ◽  
Mindlin Plate ◽  
Failure Behavior ◽  
Plate Model ◽  
Moderately Thick Plate ◽  
Mindlin Plate Theory

For hierarchical corrugated sandwich structures with second-order core, the prediction error of failure behavior by existing methods becomes unacceptable with the increase of structure thickness. In this study, a novel analytical model called moderately thick plate model is developed based on Mindlin plate theory, which can be used to analyze the failure behavior of hierarchical corrugated structures with second-order core under compression or shear loads. Then, the analytical expressions of nominal stress for six competing failure modes are derived based on the moderately thick plate model. The results of six different unit structures based on the moderately thick plate model agree quite well the ones by finite element methods. Furthermore, the influence of different structure thicknesses is investigated to validate the applicability of the moderately thick plate model. According to the comparative results with the thin plate model, the proposed moderately thick plate model has a better precision with the increase of the ratio of thickness to width for failure components.

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.

scholarly journals Analysis Bending Solutions of Clamped Rectangular Thick Plate

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yang Zhong ◽  
Qian Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Shear Deformation ◽  
Thick Plate ◽  
Plate Theory ◽  
Analytic Solutions ◽  
Higher Order ◽  
Numerical Comparison ◽  
Governing Equations ◽  
Partial Differential

The bending solutions of rectangular thick plate with all edges clamped and supported were investigated in this study. The basic governing equations used for analysis are based on Mindlin’s higher-order shear deformation plate theory. Using a new function, the three coupled governing equations have been modified to independent partial differential equations that can be solved separately. These equations are coded in terms of deflection of the plate and the mentioned functions. By solving these decoupled equations, the analytic solutions of rectangular thick plate with all edges clamped and supported have been derived. The proposed method eliminates the complicated derivation for calculating coefficients and addresses the solution to problems directly. Moreover, numerical comparison shows the correctness and accuracy of the results.

Sign in / Sign up

Export Citation Format

Share Document