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.

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.

Effect of Stress Concentration on Laminated Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 241-252 ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal
Keyword(s):  
Stress Concentration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Normal Strain ◽  
Concentrated Load ◽  
Transverse Shear Stresses

AbstractThis paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

Stress analysis of smart composite plate structures

2020 ◽  
pp. 095440622097544
Author(s):  
Aniket Chanda ◽  
Utkarsh Chandel ◽  
Rosalin Sahoo ◽  
Neeraj Grover
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Hyperbolic Function ◽  
Solution Technique ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations

In the present study, the electro-mechanical responses of smart laminated composite plates with piezoelectric materials are derived using a two-dimensional (2 D) displacement-based non-polynomial higher-order shear deformation theory. The kinematics of the mathematical model incorporates the deformation of laminates which account for the effects of transverse shear deformation and a non-linear variation of the in-plane displacements using inverse sine hyperbolic function of the thickness coordinate. The equilibrium equations are obtained using the minimization of energy principle known as the principle of minimum potential energy (PMPE) which is also based on a variational approach and the solutions are obtained using Navier’s solution technique for diaphragm supported smart laminated composite plates. The responses obtained in the form of deflection and stresses are compared with three dimensional (3 D) solutions and also with different polynomial and non-polynomial based higher-order theories in the literature. The transverse shear stresses are obtained using 3 D equilibrium equations of elasticity to enhance the accuracy of the present results. Various examples are numerically solved to establish the efficiency of the present model.

Higher-Order Zig-Zag Theory for Laminated Composites With Multiple Delaminations

2000 ◽  
Vol 68 (6) ◽  
pp. 869-877 ◽  
Author(s):  
M. Cho ◽  
J.-S. Kim
Keyword(s):  
Displacement Field ◽  
Transverse Shear ◽  
Dynamic Equilibrium ◽  
Composite Plates ◽  
Present Theory ◽  
Higher Order ◽  
Bottom Surface ◽  
Shear Stresses ◽  
Equilibrium Equations ◽  
Natural Frequency Analysis

A higher-order zig-zag theory has been developed for laminated composite plates with multiple delaminations. By imposing top and bottom surface transverse shear stress-free conditions and interface continuity conditions of transverse shear stresses including delaminated interfaces, the displacement field with minimal degree-of-freedoms are obtained. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Through the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. The delaminated beam finite element is implemented to evaluate the performance of the newly developed theory. Linear buckling and natural frequency analysis demonstrate the accuracy and efficiency of the present theory. The present higher-order zig-zag theory should work as an efficient tool to analyze the static and dynamic behavior of the composite plates with multiple delaminations.

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.

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.

scholarly journals Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
B. Sidda Reddy ◽  
J. Suresh Kumar ◽  
C. Eswara Reddy ◽  
K. Vijaya Kumar Reddy
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Transverse Shear Stresses

The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The equations of motion and boundary conditions are derived using the principle of virtual work. Solutions are obtained for FGPs in closed-form using Navier’s technique. Comparison studies are performed to verify the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the buckling behavior of functionally graded plates. The effect of side-to-thickness ratio, aspect ratio, modulus ratio, the volume fraction exponent, and the loading conditions on the critical buckling load of FGPs is also investigated and discussed.

scholarly journals A Predictor-Corrector Layerwise Model for Thick Laminated Composite Plates and Shells: Bending and Vibration

1997 ◽  
Author(s):  
K. H. Lee ◽  
L. Cao
Keyword(s):  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations ◽  
Model Account ◽  
Transverse Shear Stresses ◽  
Plates And Shells ◽  
Predictor Corrector

This paper describes a predictor-corrector theory based on a general higher-order layerwise model for the accurate prediction of the linear static and dynamic response of thick laminated composite plates and shells. The general polynomials introduced in the model account for the arbitrary variation of the transverse shear stresses across the thickness of each layer. The main purpose of the approach is to reduce the differences between the assumed variation of the transverse shear stresses provided by the constitutive equations and the computed variation of the same stresses from the equilibrium equations of elasticity. The present predictor-corrector layerwise model satisfies the continuity of the in-plane displacements and the transverse shear stresses at the interfaces. The numerical results for the bending and vibration of thick laminated composite plates and shells show that a high level of accuracy can be achieved with the same number of variables as that in Mindlin’s theory.

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