Structural Analysis of Variable Stiffness Laminated Plates Using First-Order Shear Deformation Theory

2014 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
M. Arian Nik ◽  
D. Pasini
Keyword(s):  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Buckling Load ◽  
Shear Stresses ◽  
Critical Buckling Load ◽  
First Order ◽  
Stiffness Design ◽  
Transverse Shear Stresses

Constant and variable stiffness strategies have been developed to design a composite laminate. With the former, each layer is designed with straight fibers that have the highest stiffness and strength in the fiber direction. With the latter, on the other hand, the stiffness can change within each layer by placing the fibers along a curvilinear fiber path. A variable stiffness design results in improved structural performance, as well as opens up opportunities to search for trade-off among structural properties. During the manufacture of a variable stiffness design with Automated Fiber Placement, certain defects in the form of gaps and overlaps could appear within the laminate and affect the laminate performance. In this study, we use the first-order shear deformation theory to assess the effect of transverse shear stresses on the critical buckling load, free and forced vibration of a variable stiffness laminate with embedded defects, an issue so far rarely examined in literature. The governing differential equations for the static analysis are first derived. A semi-analytic solution is then obtained using the hybrid Fourier-Galerkin method and the numeric time integration technique. The eigenvalue analysis is also conducted to determine the fundamental frequency and critical buckling load of the plate. It is found that the behavior of a variable stiffness plate is much more affected by the shear stresses than a constant stiffness plate. Ignoring the effect of transverse shear stresses results in 34% error in the predicted buckling load of a variable stiffness laminate with overlaps and a length-to-thickness ratio of 10.

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.

scholarly journals A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2385 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Nguyen Dinh Quang ◽  
Do Van Thom
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Shear Stresses ◽  
Transverse Shear Strain ◽  
First Order ◽  
Advanced Composite

A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

Mechanical Buckling of Functionally Graded Cylindrical Shells Based on the First Order Shear Deformation Theory

2007 ◽  
Author(s):  
Ramin Narimani ◽  
Mehdi Karami Khorramabadi ◽  
Payam Khazaeinejad
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Form Solution ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
First Order

Buckling analysis of simply supported functionally graded cylindrical shells under mechanical loads is presented in this paper. The Young’s modulus of the shell is assumed to vary as a power form of the thickness coordinate variable. The shell is assumed to be under three types of mechanical loadings, namely, axial compression, uniform external lateral pressure, and hydrostatic pressure loading. The equilibrium and stability equations are derived based on the first order shear deformation theory. Resulting equations are employed to obtain the closed-form solution for the critical buckling load. The influences of dimension ratio, relative thickness and the functionally graded index on the critical buckling load are studied. The results are compared with the known data in the literature.

Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory

2018 ◽  
Vol 22 (7) ◽  
pp. 2186-2209 ◽  
Author(s):  
Saeed Amir ◽  
Mohammad Khorasani ◽  
Hassan BabaAkbar-Zarei
Keyword(s):  
Aspect Ratio ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Sandwich Plate ◽  
Piezoelectric Materials ◽  
Shear Deformation Theory ◽  
Buckling Load ◽  
Sandwich Plates ◽  
Critical Buckling Load ◽  
First Order

In piezoelectric materials and at the nano-scale, there is a coupling between electrical polarization and strain gradients fields, which is called flexoelectricity. The effects of this phenomenon seem to be negligible in micro/macro scales. The current study has attempted to have a cohesive concentration on the buckling behaviors of sandwich plates. To achieve the abovementioned aim with a higher accuracy, the flexoelectric effect assumes to be existing on the top and bottom face sheets and the core is a composite plate. Also, based on statistics, the first-order shear deformation theory seems to lead to more accurate results. Therefore, in the present research we follow this method to obtain results. The analytical method is applied to solve higher order governing equations. In addition, the critical buckling voltage is calculated considering the flexoelectricity, and it is found that the effects of flexoelectricity play significant roles in determining the critical buckling voltage. Moreover, it is revealed that the thickness of the flexoelectric face sheets and the aspect ratio of the sandwich plate play the same role in critical buckling load variations. It means that the critical buckling load decreases when the thickness of the flexoelectric face sheets or the aspect ratio of the sandwich plate increases and vice versa. The results of the present work can be used for the optimum design and control of similar systems such as micro-electro-mechanical and nano-electromechanical devices.

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.

Geometrically nonlinear finite element simulation of smart laminated shells using a modified first-order shear deformation theory

2019 ◽  
Vol 30 (4) ◽  
pp. 517-535 ◽  
Author(s):  
Hanen Mallek ◽  
Hanen Jrad ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Piezoelectric Materials ◽  
Shear Deformation Theory ◽  
Nonlinear Finite Element ◽  
Shear Stresses ◽  
Geometrically Nonlinear ◽  
Element Analysis ◽  
First Order

This article investigates geometrically nonlinear and linear analysis of multilayered shells with integrated piezoelectric materials. An efficient nonlinear shell element is developed to solve piezoelastic response of laminated structure with embedded piezoelectric actuators and sensors. A modified first-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The electric potential is assumed to be a linear function through the thickness of each active sub-layer. Several numerical tests for different piezolaminated geometries are conducted to highlight the reliability and efficiency of the proposed implementation in linear and geometrically nonlinear finite element analysis.

Effect of Transverse Shear on Deformation of Thick Laminated Sandwich Plates

2006 ◽  
Vol 324-325 ◽  
pp. 279-282
Author(s):  
K. Gordnian ◽  
H. Hadavinia ◽  
J. Karwatzki
Keyword(s):  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Sandwich Plates ◽  
Maximum Deflection ◽  
Transverse Shear Stress ◽  
Cylindrical Bending ◽  
Element Analysis ◽  
Geometrical Properties ◽  
First Order

The effect of transverse shear on the deformation of thick laminated sandwich plates under cylindrical bending is studied, based on the first order shear deformation theory (FSDT) with the application of shear correction factor (SCF). It is shown that depending on the mechanical and geometrical properties of the layers, the contribution of the transverse shear stress to the maximum deflection of the plate is variable and in some cases accounts for up to around 88% of the total deflection. The analytical results are compared and verified with finite element analysis.

A Unified Shear Deformation Theory for the Bending of Isotropic, Functionally Graded, Laminated and Sandwich Beams and Plates

2017 ◽  
Vol 09 (01) ◽  
pp. 1750007 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Present Theory ◽  
Functionally Graded ◽  
Shear Stresses

In this paper, a displacement-based unified shear deformation theory is developed for the analysis of shear deformable advanced composite beams and plates. The theory is developed with the inclusion of parabolic (PSDT), trigonometric (TSDT), hyperbolic (HSDT) and exponential (ESDT) shape functions in terms of thickness coordinate to account for the effect of transverse shear deformation. The in-plane displacements consider the combined effect of bending rotation and shear rotation. The use of parabolic shape function in the present theory leads to the Reddy’s theory, but trigonometric, hyperbolic and exponential functions are first time used in the present displacement field. The present theory is accounted for an accurate distribution of transverse shear stresses through the thickness of plate, therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived from the principle of virtual work. Navier type closed-form solutions are obtained for simply supported boundary conditions. To verify the global response of the present theory it is applied for the bending of both one-dimensional (beams) and two-dimensional (plates) functionally graded, laminated composite and sandwich structures. The present results are compared with exact elasticity solution and other higher order shear deformation theories to verify the accuracy and efficiency of the present theory.

The Influence of First Order Shear Deformation on Dynamic Buckling of Composite Bar

2015 ◽  
Vol 751 ◽  
pp. 195-199 ◽  
Author(s):  
Long Fei Wang ◽  
Zhi Jun Han ◽  
Xiao Peng Yan ◽  
Guo Yun Lu
Keyword(s):  
Shear Deformation ◽  
Linear Equations ◽  
Shear Deformation Theory ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Stress Wave Propagation ◽  
Critical Buckling Load ◽  
First Order ◽  
Homogeneous Linear ◽  
Reddy Theory

Taking stress wave propagation into account, the governing equations of composite bar with the clamped-fixed boundary conditions considering FSDT (first order shear deformation theory) are derived on the basis of Reddy’ theory and solved by the variable-separated method. The analytic expression of the critical buckling load is obtained basing on the characteristics of homogeneous linear equations having nonzero-solution. The results of the theoretical study and the numerical calculation indicate that FSDT has influence on dynamic buckling of composite bar, and the critical buckling load is small when FSDT is considered. They also show that the magnitude of effect taken by FSDT is small when the layer angle is big.

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