STRESS ANALYSIS OF THICK LAMINATED PLATES USING TRIGONOMETRIC SHEAR DEFORMATION THEORY

2013 ◽  
Vol 05 (01) ◽  
pp. 1350003 ◽  
Author(s):  
YUWARAJ M. GHUGAL ◽  
ATTESHAMUDDIN S. SAYYAD
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Strain Effect ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Deformation Effect ◽  
Line Load ◽  
Transverse Normal Strain

A trigonometric shear deformation theory (TSDT) taking into account transverse shear deformation effect as well as transverse normal strain effect is presented. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in thickness coordinates is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The results of displacements and stresses for static flexure of simply supported symmetric and anti-symmetric cross-ply laminated square plates subjected to parabolic load and line load are obtained. The results obtained by present theory are compared with those of classical, first-order and higher-order plate theories.

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 NEW SIMPLE HYPERBOLIC SHEAR DEFORMATION THEORY FOR FUNCTIONALLY GRADED PLATES RESTING ON WINKLER–PASTERNAK ELASTIC FOUNDATIONS

2014 ◽  
Vol 11 (06) ◽  
pp. 1350098 ◽  
Author(s):  
ABDERRAHMANE SAID ◽  
MOHAMMED AMEUR ◽  
ABDELMOUMEN ANIS BOUSAHLA ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Governing Equations ◽  
Pasternak Elastic Foundation ◽  
Shear Deformation Theories

An improved simple hyperbolic shear deformation theory involving only four unknown functions, as against five functions in case of first or other higher-order shear deformation theories, is introduced for the analysis of functionally graded plates resting on a Winkler–Pasternak elastic foundation. The governing equations are derived by employing the principle of virtual work and the physical neutral surface concept. The accuracy of the present analysis is demonstrated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories.

Using Hyperbolic Shear Deformation Theory for Study and Analysis, the Thermal Bending of Functionally Graded Sandwich Plate Properties

2019 ◽  
Vol 12 (4) ◽  
pp. 326-338
Author(s):  
Bendahane Khaled ◽  
Bouguenina Otbi ◽  
Mokaddem Allel ◽  
Doumi Bendouma ◽  
Belakhdar Khalil
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Thermal Loading ◽  
Sandwich Plate ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Hard Core ◽  
Functionally Graded ◽  
Thermal Bending ◽  
Plate Aspect Ratio

Background: Several studies and patents have been carried out on the realization and optimization of structures and structural elements subjected to several-weights-critical-applications. Among the structures optimized in engineering, there are sandwich structures that are mainly used to react under these conditions. Objective: In this article, we have investigated the thermal bending response of simply supported Functionally Graded Sandwich Plate (FGSP). Methods: Using simple Hyperbolic Shear Deformation Theory (HSDT). A type of FGSP with both functionally graded materiel FGM face and ceramic hard core are considered. Based on the principle of virtual work, the governing equations are derived and then these equations are solved via Navier procedure. Analytical solutions are obtained to predict the deflection, axial and shear stress of FGSP. Results: To verify the efficiency of the present method a comparison with existing literature and patents results is employed. The influence of the plate aspect ratio, the relative thickness, the gradient index, the sandwich plate schemes, and the thermal loading conditions on the bending of FGSP are investigated. Conclusion: A good agreement is obtained between present results and the existing literature solutions. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded sandwich plates. Various patents have been discussed.

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

2017 ◽  
Vol 21 (8) ◽  
pp. 2751-2778 ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M Zenkour
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Size Dependent ◽  
Magnetic Potentials ◽  
Sinusoidal Shear Deformation Theory

In this work, an analytical solution for bending analysis of the three-layer curved nanobeams is presented. The nanobeams are including a nanocore and two piezomagnetic face-sheets. The structure is subjected to applied electric and magnetic potentials while is resting on Pasternak's foundation. To reach more accurate results, sinusoidal shear deformation theory is employed to derive displacement field of the curved nanobeams. In addition, nonlocal electro-magneto-elasticity relations are employed to derive governing equations of bending based on the principle of virtual work. The analytical results are presented for simply supported curved nanobeam to discuss the influence of important parameters on the vibration and bending results. The important parameters are included spring and shear parameters of the foundation, applied electric and magnetic potentials, nonlocal parameter, and radius of curvature of curved nanobeam.

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.

Analysis of Deflections and Stresses for Laminated Composite Plates Based on a New Higher-Order Shear Deformation Theory

2012 ◽  
Vol 226-228 ◽  
pp. 1725-1729 ◽  
Author(s):  
Xiang Jun Lan ◽  
Zhi Hua Feng
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
First Order ◽  
Shear Deformation Theories

Based on the new simple third-order shear deformation theory, the deflections and stresses of the simply surported symmetrical laminated composite plates are obtained by using the principle of virtual work .The solutions are compared with the solutions of three-dimensional elasticity theory, the first-order shear deformation theory and the Reddy’s higher order shear deformation theory . Results show that the presented new theory is more reliable, accurate, and cost-effective in computation than the first-order shear deformation theories and other simple higher-order shear deformation theories.

scholarly journals Analysis of non symmetric FG sandwich plates under Thermo-mechanical loading using a novel shear deformation theory with stretching effect

2018 ◽  
Vol 241 ◽  
pp. 01018
Author(s):  
H. Saidi ◽  
A. Bouchafa ◽  
A. Tounsi ◽  
A. E.A. Adda.Bedia
Keyword(s):  
Shear Deformation ◽  
Mechanical Loading ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Sandwich Plates ◽  
Closed Form Solutions ◽  
Stretching Effect

The analysis of non-symmetric functionally graded sandwich plates under thermo-mechanical loading is developed using a novel hyperbolic shear deformation theory and considering thickness stretching effects. This theory accounts for adequate distribution of the transverse shear strains in the thickness of the plate and satisfies the traction free boundary conditions on the top and bottom surface of the plates, thus a shear correction factor is not required. The governing equations of equilibrium of non-symmetric functionally graded sandwich plates can be obtained using virtual work principle and the closed form solutions are obtained by using Navier technique. The accuracy of the present results is established by comparing those with well known trigonometric shear deformation theories. The results are presented for deflections and stresses of non-symmetric simply supported square plates.

A non-polynomial axiomatic framework for modelling and bending analysis of doubly curved spherical and cylindrical shells: An analytical solution

2021 ◽  
pp. 146442072110235
Author(s):  
Lalit K Sharma ◽  
Neeraj Grover ◽  
Ashish Purohit ◽  
Rosalin Sahoo
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Cylindrical Shells ◽  
Mathematical Formulation ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Shells ◽  
Doubly Curved ◽  
Laminated Composite Shells

In the present work, the doubly curved spherical and cylindrical laminated composite shells are modelled and analysed in the framework of non-polynomial axiomatic approach. The inverse hyperbolic shear deformation theory originally developed for the laminated composite plates is extended to model the deformation characteristics of laminated composite shells. The mathematical formulation is developed under the assumption of linear structural kinematics and linear-elastic-orthotropic material behaviour. The governing equations of the model are obtained using the principle of virtual work and solved in exact manner for simply supported boundary conditions following the Navier solution methodology. The bending response of thick and thin spherical and cylindrical shells subjected to different types of transverse loads such as point load, uniform load and sinusoidal load is analysed in the framework of developed methodology. The obtained results due to inverse hyperbolic shear deformation theory are compared with other shell theories and on the basis of this comparison, the validity and applicability of the inverse hyperbolic shear deformation theory for doubly curved spherical and cylindrical shells is ensured.

A HYPERBOLIC SHEAR DEFORMATION THEORY FOR FLEXURE AND VIBRATION OF THICK ISOTROPIC BEAMS

2009 ◽  
Vol 06 (04) ◽  
pp. 585-604 ◽  
Author(s):  
YUWARAJ MAROTRAO GHUGAL ◽  
RAJNEESH SHARMA
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Correction Factor ◽  
Displacement Field ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Flexural Vibration ◽  
Shear Correction Factor

A Hyperbolic Shear Deformation Theory taking into account transverse shear deformation effects, is presented for the static flexure and free flexural vibration analysis of thick isotropic beams. The displacement field of the theory contains two variables and does not require shear correction factor. The hyperbolic sine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The most important feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relation, satisfying the stress free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for flexure and free vibration of simply supported uniform, isotropic beams are compared with those of elementary, refined, and exact beam theories to validate the accuracy of the theory.

scholarly journals Numerical Analysis of Thick Isotropic and Transversely Isotropic Plates in Bending using FE Based New Inverse Shear Deformation Theory

2021 ◽  
Vol 18 (3) ◽  
pp. 8882-8894
Author(s):  
DHIRAJ BHASKAR ◽  
Ajaykumar G. Thakur ◽  
Imran I. Sayyad ◽  
Santosh V. Bhaskar
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Present Theory ◽  
Displacement Function ◽  
Simply Supported

In this work, using new inverse trigonometric kinematic displacement function, the bending solution of simply supported isotropic and transversely isotopic thin, moderately thin and thick square plates with aspect ratio variations is given. The paper introduces a new inverse trigonometric shear deformation theory (nITSDT) for the bi-directional bending study, which is variationally compatible. The transverse shear stress can be obtained directly from the constitutive relationships on the top and bottom surfaces of the plate that satisfy the shear stress free surface conditions, so the theory does not need a factor for shear correction. The dynamic version of the virtual work principle is used to obtain the governing equations and boundary conditions of the theory. The Finite Element (FE) solution has been developed using MATLAB code based on the present theory for simply supported laminated composite plates. In order to illustrate the efficiency of the proposed theory, the results of displacements and stresses are compared with those of other refined theories and exact solution. The findings obtained from the use of the theory are found to agree well with the precise results of elasticity.

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