scholarly journals On the deformation of laminated composite and sandwich curved beams

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Pravin V. Avhad ◽  
Atteshamuddin S. Sayyad
Keyword(s):  
Boundary Conditions ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Deformation Analysis ◽  
Solution Technique ◽  
Curved Beams ◽  
Simply Supported ◽  
Fifth Order

Abstract Plenty of research articles are available on the static deformation analysis of laminated straight beams using refined shear deformation theories. However, research on the deformation of laminated curved beams with simply supported boundary conditions is limited and needs more attention nowadays. With this objective, the present study deals with the static analysis of laminated composite and sandwich beams curved in elevation using a new quasi-3D polynomial type beam theory. The theory considers the effects of both transverse shear and normal strains, i.e. thickness stretching effects. In the present theory, axial displacement has expanded up to the fifth-order polynomial in terms of thickness coordinates to effectively account for the effects of curvature and deformations. The present theory satisfies the zero traction boundary condition on the top and bottom surfaces of the beam. Governing differential equations and associated boundary conditions are established by using the Principal of virtual work. Navier’s solution technique is used to obtain displacements and stresses for simply supported beams curved in elevation and subjected to uniformly distributed load. The present results can be benefited to the upcoming researchers.

scholarly journals Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal ◽  
N. S. Naik
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Transverse Displacement ◽  
Sandwich Beams ◽  
Bending Analysis

AbstractA trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

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.

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.

scholarly journals Flexural Interpretation of Simply Supported Laminated Composite Beam

2020 ◽  
Vol 8 (5) ◽  
pp. 3559-3565
Keyword(s):  
Shear Deformation ◽  
Composite Beam ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Shear Stresses ◽  
Bending Stress ◽  
Simply Supported ◽  
Laminated Composite Beam ◽  
Laminated Composite Beams

In this Paper, the analysis of simply supported laminated composite beam having uniformly distributed load is performed. The solutions obtained in the form of the displacements and stresses for different layered cross ply laminated composite simply supported beams subjected uniformly distributed to load. Different aspect ratio consider for different results in terms of displacement, bending stress and shear stresses. The shear stresses are calculated with the help of equilibrium equation and constitutive relationship. Using displacement field including trigonometric function of laminated composite beams are derived from virtual displacement principle. There are axial displacement, transverse displacement, bending stress and shear stresses. In addition, Euler-Bernoulli (ETB), First order shear deformation beam theory (FSDT), Higher order shear deformation beam theory (HSDT) and Hyperbolic shear deformation beam theory (HYSDT) solution have been made for comparison and better accuracy of solutions and results of static analyses of laminated composite beams for simply supported laminated composite beam.

Free vibration and buckling analysis of laminated composites and sandwich microbeams using a transverse shear-normal deformable beam theory

2019 ◽  
Vol 26 (3-4) ◽  
pp. 214-228 ◽  
Author(s):  
Armagan Karamanli ◽  
Metin Aydogdu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transverse Shear ◽  
Couple Stress Theory ◽  
Laminated Composite ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Aspect Ratios

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios.

scholarly journals Thermal Buckling of Piezoelectric Composite Beam

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
S. Yazdani ◽  
Y. Kiani ◽  
M. Jabbari ◽  
M. R. Eslami
Keyword(s):  
Boundary Conditions ◽  
Composite Beam ◽  
Thermal Loading ◽  
Laminated Composite ◽  
Beam Theory ◽  
Piezoelectric Composite ◽  
Closed Form Solutions ◽  
Beam Geometry ◽  
Piezoelectric Layers ◽  
Beam Thickness

Buckling analysis of laminated composite beams with piezoelectric layers subjected to thermal loading and constant voltage is studied. The material properties are assumed to be homogeneous in any layer through the beam thickness. The first-order beam theory and nonlinear strain-displacement relation are used to obtain the governing equations of the composite beam. The beam is assumed under uniform type of thermal loading and various types of boundary conditions. For each case of boundary conditions, closed-form solutions are obtained. The effects of the applied actuator voltage, beam geometry, and boundary conditions on the buckling temperature are investigated.

Interaction Curves for Shear and Bending of Plastic Beams

1957 ◽  
Vol 24 (3) ◽  
pp. 453-456
Author(s):  
P. G. Hodge
Keyword(s):  
General Formula ◽  
Plane Stress ◽  
Elementary Theory ◽  
Beam Theory ◽  
Present Theory ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Interaction Curves

Abstract Interaction curves are presented for plastic beams subject to combined shear and bending. A general formula is obtained and specific curves are drawn for rectangular and I-sections. A simply supported beam with a concentrated load is considered as an example. The results are compared with those of simple beam theory and with available plane-stress solutions. It is concluded that the elementary theory is adequate for height-to-length ratios of less than 0.1, while the present theory is useful in the range from 0.1 to 1.0.

SOUND TRANSMISSION ACROSS A FINITE SIMPLY SUPPORTED DOUBLE-LAMINATED COMPOSITE PLATE WITH ENCLOSED AIR CAVITY

2019 ◽  
Vol 57 (6) ◽  
pp. 749
Author(s):  
Pham Ngoc Thanh ◽  
Tran Ich Thinh
Keyword(s):  
Boundary Conditions ◽  
Composite Plate ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Laminated Composite ◽  
Acoustic Vibration ◽  
Potential Method ◽  
Laminated Composite Plate ◽  
Air Cavity ◽  
Simply Supported

ABSTRACTSound transmission across a finite orthotropic laminated double-composite plate with enclosed air cavity on an infinite acoustic rigid baffle is investigated analytically. Sound velocity potential method combined with simply supported boundary conditions is used instead of traditional methods, has good scalability and is important for studies of acoustic vibration of structures. The sound transmission loss is calculated from the ratio of incident to transmitted acoustic powers. Specifically, the focus is placed on the effects of several key system parameters on sound transmission including the plate dimensions, the laminate configurations, the boundary conditions, and the composite materials are systematically examined.

Strain Gradient Finite Element Analysis on the Vibration of Double-Layered Graphene Sheets

2016 ◽  
Vol 13 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Wei Xu ◽  
Lifeng Wang ◽  
Jingnong Jiang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Strain Gradient ◽  
Virtual Work ◽  
Gradient Elasticity ◽  
Kirchhoff Plate ◽  
Small Scale ◽  
Graphene Sheets ◽  
Simply Supported

A nonlocal Kirchhoff plate model with the van der Waals (vdW) interactions taken into consideration is developed to study the vibration of double-layered graphene sheets (DLGS). The dynamic equations of multi-layered Kirchhoff plate are derived based on strain gradient elasticity. An explicit formula is derived to predict the natural frequency of the DLGS with all edges simply supported. Then a 4-node 24-degree of freedom (DOF) Kirchhoff plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration by the theory of virtual work. It can be directly used to predict the scale effect on the vibrational DLGS with different boundary conditions. A good agreement between finite element method (FEM) results and theoretical natural frequencies of the vibration simply supported double-layered graphene sheet (DLGS) validates the reliability of the FEM. Finally, this new FEM is used to investigate the effect of vdW coefficients, sizes, nonlocal parameters, vibration mode and boundary conditions on the vibration behaviors of DLGS.

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