Efficient Laminate Theory for Predicting Transverse Shear Stresses in Piezoelectric Composite Plates

AIAA Journal ◽  
2009 ◽  
Vol 47 (12) ◽  
pp. 3022-3030 ◽  
Author(s):  
S. Kapuria ◽  
J. K. Nath
Keyword(s):  
Transverse Shear ◽  
Composite Plates ◽  
Piezoelectric Composite ◽  
Shear Stresses ◽  
Laminate Theory ◽  
Transverse Shear Stresses

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.

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.

Determination of the transverse shear stress in layered composites

2020 ◽  
Vol 86 (2) ◽  
pp. 44-53
Author(s):  
Yu. I. Dudarkov ◽  
M. V. Limonin
Keyword(s):  
Shear Stress ◽  
Transverse Shear ◽  
Composite Beam ◽  
Layered Composite ◽  
Equivalent Model ◽  
Shear Stresses ◽  
Transverse Shear Stress ◽  
Layered Composites ◽  
Laminate Composites ◽  
Transverse Shear Stresses

An engineering approach to estimation of the transverse shear stresses in layered composites is developed. The technique is based on the well-known D. I. Zhuravsky equation for shear stresses in an isotropic beam upon transverse bending. In general, application of this equation to a composite beam is incorrect due to the heterogeneity of the composite structure. According to the proposed method, at the first stage of its implementation, a transition to the equivalent model of a homogeneous beam is made, for which the Zhuravsky formula is valid. The transition is carried out by changing the shape of the cross section of the beam, provided that the bending stiffness and generalized elastic modulus remain the same. The calculated shear stresses in the equivalent beam are then converted to the stress values in the original composite beam from the equilibrium condition. The main equations and definitions of the method as well as the analytical equation for estimation of the transverse shear stress in a composite beam are presented. The method is verified by comparing the analytical solution and the results of the numerical solution of the problem by finite element method (FEM). It is shown that laminate stacking sequence has a significant impact both on the character and on the value of the transverse shear stress distribution. The limits of the applicability of the developed technique attributed to the conditions of the validity of the hypothesis of straight normal are considered. It is noted that under this hypothesis the shear stresses do not depend on the layer shear modulus, which explains the absence of this parameter in the obtained equation. The classical theory of laminate composites is based on the similar assumptions, which gives ground to use this equation for an approximate estimation of the transverse shear stresses in in a layered composite package.

Stress Singularity of Edge Delamination in Angle-Ply and Cross-Ply Laminates

1997 ◽  
Vol 64 (3) ◽  
pp. 525-531 ◽  
Author(s):  
Wen-Hwa Chen ◽  
Tain-Fu Huang
Keyword(s):  
Transverse Shear ◽  
Axial Strain ◽  
Stress Singularity ◽  
Shear Stresses ◽  
Explicit Solutions ◽  
Real Constant ◽  
Stress Singularities ◽  
General Solutions ◽  
Transverse Shear Stresses ◽  
Edge Delamination

By utilizing the general solutions derived for the plies with arbitrary fiber orientations under uniform axial strain (Huang and Chen, 1994), the explicit solutions of the edge-delamination stress singularities for the angle-ply and cross-ply laminates are obtained. The dominant edge-delamination stress singularities for the angle-ply laminates are found to be a real constant, −1/2, and a pair of complex conjugates, −1/2±i/2πln{(b+b2−a2)/a}. For the cross-ply laminates, the significant effect of transverse shear stresses of the laminate is considered and the dominant edge-delamination stress singularities are shown as −1/2 and −1/2±i/2πln{(c2+c22−4c1c3)/2c1}. a, b, cl, c2, and c3 are the corresponding combined complex constants. In addition, two elementary forms of edge-delamination stress singularity, say, r−1/2 and rδr(lnr)n(δr=n−3/2,n=1,2...) exist for both the angle-ply and cross-ply laminates. Excellent correlations between the present results and available solutions show the validity of the approach. The deficiencies of the solutions available in the literature are compensated. New results for other angle-ply and cross-ply laminates are also provided.

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.

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.

Bending Analysis of SMA Embedded Rectangular Laminated Sandwich Plates with Soft Core Using 3D Finite Element Method

2011 ◽  
Vol 110-116 ◽  
pp. 1458-1465 ◽  
Author(s):  
M. Khadem ◽  
M. M. Kheirikhah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transverse Shear ◽  
Soft Core ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
3D Finite Element ◽  
Bending Analysis ◽  
Transverse Shear Stresses ◽  
3D Finite Element Method

Nowadays Shape Memory Alloys (SMAs) are used as actuators in many applications such as aerospace structures. In sandwich structures, the SMA wires or plates are used in the skins for shape control of the structure or vibration damping. In this paper, bending behavior of sandwich plates with embedded SMA wires in their skins is studied. 3D finite element method is used for construction and analysis of the sandwich plate with a flexible core and two stiff skins. Some important points such as continuity conditions of the displacements, satisfaction of interlaminar transverse shear stresses, the conditions of zero transverse shear stresses on the upper and lower surfaces and in-plane and transverse flexibility of soft core are considered for accurate modeling and analysis of sandwich structures. Solution for bending analysis of sandwich plates under various transverse loads are presented and the effect of many parameters such as plate dimensions, loading conditions, material properties of core, skins and SMA wires are studied. Comparison of the present results in special case with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed model.

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.

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