Three-Dimensional Elasticity Analysis of Thick Rectangular Laminated Composite Plates Using Meshless Local Petrov-Galerkin (MLPG) Method

2006 ◽  
Vol 5-6 ◽  
pp. 331-338 ◽  
Author(s):  
S.M.R. Alavi ◽  
Mohammad Mohammadi Aghdam ◽  
A. Eftekhari
Keyword(s):  
Interpolation Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Three Dimensions ◽  
Elasticity Analysis ◽  
Weak Formulation ◽  
Mlpg Method

This article presents apparently the first application of Meshless local Petrov-Galerkin (MLPG) method for 3-D elasticity analysis of moderately thick rectangular laminated plates. As with other Meshless methods, the problem domain is represented by a set of spread nodes in all three dimensions of the plate without configuration of elements. The Moving Least-Squares (MLS) method is applied to construct the required shape functions. A local asymmetric weak formulation of the problem is developed and MLPG is applied to solve the governing equations. Direct interpolation method is employed to enforce essential boundary conditions. Details of formulation, numerical procedure, convergence and accuracy characteristics of the method are investigated. Results are compared, where possible, with other analytical and numerical methods and show good agreement.

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.

Nonlinear Forced Vibrations of Laminated Piezoelectric Plates

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Muhammad Tanveer ◽  
Anand V. Singh
Keyword(s):  
Electric Fields ◽  
Mechanical Load ◽  
Numerical Procedure ◽  
Laminated Composite ◽  
Composite Plates ◽  
Forced Vibrations ◽  
Homogeneous Material ◽  
Displacement Fields ◽  
Electrical Loads ◽  
Piezoelectric Plates

A numerical approach is presented for linear and geometrically nonlinear forced vibrations of laminated composite plates with piezoelectric materials. The displacement fields are defined generally by high degree polynomials and the convergence of the results is achieved by increasing the degrees of polynomials. The nonlinearity is retained with the in-plane strain components only and the transverse shear strains are kept linear. The electric potential is approximated layerwise along the thickness direction of the piezoelectric layers. In-plane electric fields at the top and bottom surfaces of each piezoelectric sublayer are defined by the same shape functions as those used for displacement fields. The equation of motion is obtained by the Hamilton’s principle and solved by the Newmark’s method along with the Newton–Raphson iterative technique. Numerical procedure presented herein is validated by successfully comparing the present results with the data published in the literature. Additional numerical examples are presented for forced vibration of piezoelectric sandwich simply supported plates with either a homogeneous material or laminated composite as core. Both linear and nonlinear responses are examined for mechanical load only, electrical load only, and the combined mechanical and electrical loads. Displacement time histories with uniformly distributed load on the plate surface, electric volts applied on the top and bottom surfaces of the piezoelectric plates, and mechanical and electrical loads applied together are presented in this paper. The nonlinearity due to large deformations is seen to produce stiffening effects, which reduces the amplitude of vibrations and increases the frequency. On the contrary, antisymmetric electric loading on the nonlinear response of piezoelectric sandwich plates shows increased amplitude of vibrations.

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.

Three-Dimensional Plate Theory for Flexible Multibody Dynamics

2015 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Flexible Multibody Dynamics ◽  
Composite Plates ◽  
Complex Stress ◽  
Mindlin Plate ◽  
Stress States ◽  
Three Dimensional Elasticity ◽  
Material Line

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

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