The Symplectic Method for the Bending of Symmetrical Laminated Composite Plates with Clamped Boundary

2012 ◽  
Vol 479-481 ◽  
pp. 282-285
Author(s):  
Jin Guo Song ◽  
You Zhen Yang
Keyword(s):  
Separation Of Variables ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Symplectic Space ◽  
Variation Principle ◽  
Symplectic Method ◽  
Stress Distributions ◽  
Dual Variables ◽  
Function Vector

The symplectic method is applied to study analytically the stress distributions of composite laminated plates in this paper applies. The dual equations were presented by variation principle and introducing separation of variables used. Then in the symplectic space which consists of the original variables and their dual variables, the problem can be solved via effective mathematical physics methods such as the method of separation of variables and Eigen function vector expansion. The equation and Eigen-vector are deduced. The results of cross-ply laminated graphite–epoxy composite plate with clamped boundary are shown, which is compared with established results. The parameters’ influences on mechanical property are also discussed.

The Bending of Symmetrical Laminated Composite Plate Based on Symplectic Method

2011 ◽  
Vol 328-330 ◽  
pp. 1646-1649
Author(s):  
Y.Z. Yang
Keyword(s):  
Composite Plate ◽  
Separation Of Variables ◽  
Laminated Composite ◽  
Transcendental Equation ◽  
Laminated Plates ◽  
Symplectic Space ◽  
Variation Principle ◽  
Symplectic Method ◽  
Stress Distributions ◽  
Dual Variables

This paper applies a symplectic method to study analytically the stress distributions of Composite laminated plates. Using variation principle and introducing separation of variables, dual equations were presented. Then in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of sepatation of variables and eigenfunction vector expansion. The transcendental equation and eigen-vector are deduced. The results of cross-ply and angle-ply laminated graphite–epoxy composite plate are shown, which is compared with established results. The parameters’ influences on mechanical property are also discussed.

Symplectic Solutions in Singularity Problems of Anisotropic Beams

2011 ◽  
Vol 378-379 ◽  
pp. 90-93
Author(s):  
You Zhen Yang
Keyword(s):  
Separation Of Variables ◽  
Mathematical Physics ◽  
Symplectic Space ◽  
Variation Principle ◽  
Symplectic Method ◽  
Stress Distributions ◽  
Zero Eigenvalue ◽  
Numerical Examples ◽  
Localized Solutions ◽  
Dual Variables

Based on the two-dimensional elasticity,the symplectic method is applied to study analytically the stress distributions of anisotropic beam.Using variation principle and introducing separation of variables, dual equations were presented.Then in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of sepatation of variables and eigenfunction vector expansion.So the original problems come down to solve the eigensolutions of zero eigenvalue and non-zeroes eigenvalue that describe the exponentially decaying localized solutions usually ignored by Saint-Venant's principle. Completed numerical examples are newly given to compare with established results.

Symplectic Solutions in Singularity Problems of Anisotropic Beams

2011 ◽  
Vol 147 ◽  
pp. 136-139
Author(s):  
You Zhen Yang
Keyword(s):  
Separation Of Variables ◽  
Mathematical Physics ◽  
Symplectic Space ◽  
Variation Principle ◽  
Symplectic Method ◽  
Stress Distributions ◽  
Zero Eigenvalue ◽  
Numerical Examples ◽  
Localized Solutions ◽  
Dual Variables

Based on the two-dimensional elasticity,the symplectic method is applied to study analytically the stress distributions of anisotropic beam.Using variation principle and introducing separation of variables, dual equations were presented.Then in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of sepatation of variables and eigenfunction vector expansion.So the original problems come down to solve the eigensolutions of zero eigenvalue and non-zeroes eigenvalue that describe the exponentially decaying localized solutions usually ignored by Saint-Venant's principle. Completed numerical examples are newly given to compare with established results.

The Symplectic Solution for the Bi-Directional Functionally Graded Piezoelectric Materials

2012 ◽  
Vol 174-177 ◽  
pp. 131-134 ◽  
Author(s):  
Y Z Yang
Keyword(s):  
Material Properties ◽  
Piezoelectric Materials ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Symplectic Space ◽  
Variation Principle ◽  
Symplectic Method ◽  
Functionally Graded Piezoelectric Materials ◽  
Dual Variables ◽  
Functionally Graded Piezoelectric

The symplectic method is applied to study analytically the deflection field of bi-directional functionally graded piezoelectric materials in this paper. And the material properties varies exponentially both along the axial and transverse coordinates.The dual equations were presented by variation principle and introducing separation of variables used. Then in the symplectic space which consists of the original variables and their dual variables, the problem can be solved via symplectic expansion. This comparisons with experimental data were carried out to verify the validity of the symplectic method.

Determination of Vibration Source Locations in Laminated Composite Plates Using Lamb Wave Analysis

2010 ◽  
Vol 123-125 ◽  
pp. 899-902
Author(s):  
Chao Du ◽  
Qing Qing Ni ◽  
Toshiaki Natsuki
Keyword(s):  
Lamb Wave ◽  
Guided Waves ◽  
Lamb Waves ◽  
Laminated Composite ◽  
Composite Plates ◽  
Wave Dispersion ◽  
Laminated Plates ◽  
Vibration Source ◽  
Arrival Times ◽  
Wave Velocities

Signals propagate on plate-like structures as ultrasonic guided waves, and analysis of Lamb waves has been widely used for on-line monitoring. In this study, the wave velocities of symmetric and anti-symmetric modes in various directions of propagation were investigated. Since the wave velocities of these two modes are different, it is possible to compute the difference in their arrival times when these waves propagated the distance from the vibration source to sensor. This paper presents an evaluation formulation of wave velocity and describes a generalized algorithm for locating a vibration source on a thin, laminated plate. With the different velocities of two modes based on Lamb wave dispersion, the method uses two sensors to locate the source on a semi-infinite interval of a plate. The experimental procedure supporting this method employs pencil lead breaks to simulate vibration sources on quasi-isotropic and unidirectional laminated plates. The transient signals generated in this way are transformed using a wavelet transform. The vibration source locations are then detected by utilizing the distinct wave velocities and arrival times of the symmetric and anti-symmetric wave modes. The method is an effective technique for identifying impact locations on plate-like structures.

A cell-based smoothed finite element formulation for viscoelastic laminated composite plates considering hygrothermal effects

2020 ◽  
pp. 002199832098005
Author(s):  
Sy-Ngoc Nguyen ◽  
Tam T Truong ◽  
Maenghyo Cho ◽  
Nguyen-Thoi Trung
Keyword(s):  
Finite Element ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Integral Form ◽  
Complex Stress ◽  
Laminated Plates ◽  
Element Formulation ◽  
Composite Laminated Plates ◽  
Smoothed Finite Element Method

In the present study, the viscoelastic analysis is investigated for composite laminated plates using a smoothed finite element method called cell/element based smoothed discrete shear gap method. Moreover, the hygrothermal effects is considered on the viscoelastic responses of composite laminated plates. The first-order shear deformation theory is employed due to its simplicity and accuracy. With the help of the convolution theorem in Laplace transformation, the complex stress-strain relationship in integral form is simplified to linear in transformed domain. Therefore, all computing procedures are performed in the transformed domain and then, using inverse techniques (Fast Fourier Transform) to converted back to the real-time domain. The study provides an effective computational tool to analyze the viscoelastic response of laminated composite taking into account the influence of the time and hygrothermal effects.

scholarly journals Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
S. Natarajan ◽  
A.J.M. Ferreira ◽  
Hung Nguyen-Xuan
Keyword(s):  
Free Vibration ◽  
Isogeometric Analysis ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Smooth Functions ◽  
B Splines ◽  
Modification Factor ◽  
Carrera Unified Formulation ◽  
Plate Kinematics

AbstractIn this paper, we study the static bending and free vibration of cross-ply laminated composite plates using sinusoidal deformation theory. The plate kinematics is based on the recently proposed Carrera Unified Formulation (CUF), and the field variables are discretized with the non-uniform rational B-splines within the framework of isogeometric analysis (IGA). The proposed approach allows the construction of higher-order smooth functions with less computational effort.Moreover, within the framework of IGA, the geometry is represented exactly by the Non-Uniform Rational B-Splines (NURBS) and the isoparametric concept is used to define the field variables. On the other hand, the CUF allows for a systematic study of two dimensional plate formulations. The combination of the IGA with the CUF allows for a very accurate prediction of the field variables. The static bending and free vibration of thin and moderately thick laminated plates are studied. The present approach also suffers fromshear locking when lower order functions are employed and shear locking is suppressed by introducing a modification factor. The effectiveness of the formulation is demonstrated through numerical examples.

Investigation on Interlaminar Shear Stresses in Laminated Composite Plates under Thermal and Mechanical Loading

2014 ◽  
Vol 592-594 ◽  
pp. 451-455
Author(s):  
Nagaraj Murugesan ◽  
Vasudevan Rajamohan
Keyword(s):  
Finite Element ◽  
Thermal Environment ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Interlaminar Stresses ◽  
Composite Laminated Plates ◽  
Interlaminar Shear

In this study the combined effect of thermal environment and mechanical loadings on the interlaminar shear stresses of both moderately thin and thick composite laminated plates are numerically analyzed. The finite element modeling of laminated composite plates and analysis of interlaminar stresses are performed using the commercially available software package MSC NASTRAN/PATRAN. The validity of the present finite element analysis is demonstrated by comparing the interlaminar stresses developed due to mechanical loadings derived using the present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of thermal environment on interlaminar stresses generated in asymmetric cross-ply composite laminated plates of different length to thickness ratios (L/H) and boundary conditions with identical mechanical loadings. It is observed that the elevated thermal environment under identical mechanical loading lead to higher interlaminar shear stresses varying with length to depth ratio and boundary conditions in asymmetric cross-ply laminated composite plates.

scholarly journals Nonlinear Free Vibration for Viscoelastic Moderately Thick Laminated Composite Plates with Damage Evolution

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Y. F. Zheng ◽  
L. Q. Deng
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Superposition Principle ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Damage Effect ◽  
Laminated Composite Plates ◽  
Nonlinear Free Vibration ◽  
The Galerkin Method

The nonlinear free vibration for viscoelastic cross-ply moderately thick laminated composite plates under considering transverse shear deformation and damage effect is investigated. Based on the Timoshenko-Mindlin theory, strain-equivalence hypothesis, and Boltzmann superposition principle, the nonlinear free vibration governing equations for viscoelastic moderately thick laminated plates with damage are established and solved by the Galerkin method, Simpson integration, Newton-Cotes, Newmark, and iterative methods. In the numerical results, the effects of transverse shear, material viscoelasticity, span-thickness ratio, aspect ratio, and damage effect on the nonlinear free vibrating frequency of the viscoelastic cross-ply moderately thick laminated plates are discussed.

Buckling analysis of anti-symmetric cross and angle-ply laminated composite plates

2018 ◽  
Vol 106 (2) ◽  
pp. 205
Author(s):  
L. Bouyaya
Keyword(s):  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Longitudinal Direction ◽  
Laminated Plates ◽  
Buckling Load ◽  
Governing Equations ◽  
Navier Solution ◽  
Buckling Behavior ◽  
Important Progress

This article has for objective to analyze the buckling behavior of the unidirectional laminated plates. In this purpose, we propose an analytically method, based on the theory of classical, orthotropic plate theory. The governing equations are solved using Navier solution for uniform uniaxial loading in longitudinal direction. We were interested to identify the critical buckling load for simply supported antisymmetric cross-ply and antisymmetric angle-ply laminates of rectangular shape. Some important progress has been made on these relatively complicated buckling problems, involving coupling between bending and midplane stretching during a buckling deformation. Effects of different parameters such as fiber orientation angles, aspect ratio, modular ratio and number of layers were examined. Results are presented in the form of plots showing the variation in non-dimensional buckling load.

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