The Interlaminar Stresses Analysis of Composite Laminated Plates Based on the Generalized Higher-Order Global-Local Plate Theory

2013 ◽  
Vol 785-786 ◽  
pp. 239-243
Author(s):  
Wei Dong Chen ◽  
Ping Jia ◽  
Jian Cao Li ◽  
Feng Chao Zhang ◽  
Yan Chun Yu ◽  
...  
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Fortran Program ◽  
Laminated Plates ◽  
Local Theory ◽  
Shear Stresses ◽  
Interlaminar Stresses ◽  
Integration Problem ◽  
Triangular Area

A generalized higher-order global-local theory was presented. The transverse shear stresses can be got directly through the constitutive equation without using the equilibrium equation. The second derivative of interpolation function was deduced. The hammer integration of triangular area coordinate method was applied to solve the multiple integration problem of the element stiffness matrix. The order choice of numerical integration was discussed and results obtained through two different integration orders were compared. The flow of how to compile a FORTRAN program was given. A moderately thick composite laminated plate was analyzed via finite element method (FEM) based on the theory and results were compared with that of Paganos three-dimensional elasticity. It shows that the interlaminar stresses are accurate for moderately thick laminated plates.

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

Higher Order Global-Local Theory Coupled Bending and Extension for Laminated Composite Plates and Refined Element Methods

2006 ◽  
Author(s):  
Wanji Chen ◽  
Zhen Wu
Keyword(s):  
Transverse Shear ◽  
Composite Plates ◽  
Higher Order ◽  
Laminated Plates ◽  
Triangular Element ◽  
Local Theory ◽  
Weak Continuity ◽  
Shear Stresses ◽  
Thickness Direction ◽  
Transverse Shear Stresses

In this paper an augmented higher order global-local theories are presented to analyze the laminated plate problems coupled bending and extension. The in-plane displacement field is composed of a mth-order (9 > m > 3) polynomial of global coordinate z in the thickness direction and 1,2-3 order power series of local coordinate ζk in the thickness direction of each layer and a nth-order (5 > n >= 0) polynomial of global coordinate z in the thickness direction of transverse deflection. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this theory, a refined three-node triangular element satisfying the requirement of C1 weak-continuity is presented. Numerical results show that present theory can be used to predict accurately in-plane stresses and transverse shear stresses from direct use of the relations of stresses and strains without any postprocessing method. However, to accurately obtain transverse normal stresses, the local equilibrium equation approach in one element is employed herein. It is effective when the number of layers of laminated plates is more than five and up to fourteen, and it can solve the problems for coupling bending and extension. It is also shown that the present refined triangular element possesses higher accuracy.

Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory

2008 ◽  
Vol 222 (8) ◽  
pp. 1443-1452 ◽  
Author(s):  
M K Pandit ◽  
A H Sheikh ◽  
B N Singh
Keyword(s):  
Transverse Shear ◽  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Thickness Variation ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Zigzag Theory ◽  
Three Dimensional Elasticity

This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.

scholarly journals Vibration of Antisymmetric Angle-Ply Laminated Plates of Higher-Order Theory with Variable Thickness

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
A. K. Nor Hafizah ◽  
J. H. Lee ◽  
Z. A. Aziz ◽  
K. K. Viswanathan
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Plate Theory ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Transverse Shear Stresses ◽  
Thickness Variations ◽  
Higher Order Theory

Free vibration of antisymmetric angle-ply laminated plates with variable thickness is studied. Higher-order shear deformation plate theory (HSDT) is introduced in the present method to remove the shear correction factors and improve the accuracy of transverse shear stresses. The thickness variations are assumed to be linear, exponential, and sinusoidal. The coupled differential equations are obtained in terms of displacement and rotational functions and approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically by employing the eigensolution techniques with eigenvectors as spline coefficients to obtain the required frequencies. The results of numerical calculations are presented for laminated plates with simply supported boundary conditions. Comparisons of the current solutions and those reported in literature are provided to verify the accuracy of the proposed method. The effects of aspect ratio, number of layers, ply-angles, side-to-thickness ratio, and materials on the free vibration of cylindrical plates are discussed in detail.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

Vibroacoustic Comparisons and Acoustic Power Insulation Mechanisms of Multidirectional Stiffened Laminated Plates

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
Fourier Transform ◽  
High Efficiency ◽  
Three Dimensional ◽  
Acoustic Power ◽  
Higher Order ◽  
Laminated Plates ◽  
Transverse Displacement ◽  
Third Order ◽  
First Order ◽  
Implicit Equations

Vibroacoustic characteristics of multidirectional stiffened laminated plates with or without compliant layers are explored in the wavenumber and spatial domains with the help of the two-dimensional continuous Fourier transform and discrete inverse fast Fourier transform. Implicit equations of motion for the arbitrary angle ply laminated plates are derived from the three-dimensional higher order and Reddy third order shear deformation plate theories. The expressions of acoustic power of the stiffened laminated plates with or without complaint layers are formulated in the wavenumber domain, which is a significant method to calculate acoustic power of the stiffened plates with multiple sets of cross stiffeners. Vibroacoustic comparisons of the stiffened laminated plates are made in terms of the transverse displacement spectra, forced responses, acoustic power, and input power according to the first order, Reddy third order, and three-dimensional higher order plate theories. Sound reduction profiles of compliant layers are further examined by the theoretical deductions. This study shows the feasibility and high efficiency of the first order and Reddy third order plate theories in the broad frequency range and allows a better understanding the principal mechanisms of acoustic power radiated from multidirectional stiffened laminated composite plates with compliant layers, which has not been adequately addressed in its companion paper. (Cao and Hua, 2012, “Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers,” ASME J. Vib. Acoust., 134(5), p. 051001.)

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.

Interlaminar stress analysis of multilayered composites based on the Hu-Washizu variational theorem

2017 ◽  
Vol 52 (13) ◽  
pp. 1765-1779 ◽  
Author(s):  
Wu Zhen ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Beam Element ◽  
Composite Beams ◽  
Higher Order ◽  
Shear Stresses ◽  
Interlaminar Stresses ◽  
Beam Elements ◽  
Transverse Shear Stresses ◽  
Derivatives Of

Up to date, accurate prediction of interlaminar stresses is still a challenging issue for two-node beam elements. The postprocessing approaches by integrating the three-dimensional equilibrium equation have to be used to obtain improved transverse shear stresses, whereas the equilibrium approach requires the first-order derivatives of in-plane stresses. In-plane stresses within two-node beam element are constant, so the first-derivatives of in-plane stresses are close to zero. Thus, two-node beam elements encounter difficulties for accurate prediction of transverse shear stresses by the constitutive equation or the equilibrium equation, so a robust two-node beam element is expected. A two-node beam element in terms of the global higher-order zig-zag model is firstly developed by employing the three-field Hu-Washizu mixed variational principle. By studying the effects of different boundary conditions, stacking sequence and loading on interlaminar stresses of multilayered composite beams, it is shown that the proposed two-node beam element yields more accurate results with lesser computational cost compared to various higher-order models. It is more important that accurate transverse shear stress has active impact on displacements and in-plane stresses of multilayered composite beams.

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