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.

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.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

Free and forced vibration analysis of flyash/graphene filled laminated composite plates using higher order shear deformation theory

2021 ◽  
pp. 095440622110531
Author(s):  
Sarada P Parida ◽  
Pankaj C Jena
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Low Cost ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Weight Percentage ◽  
Circular Holes ◽  
Forced Vibration Analysis

The strength of the conventional composite plates can be enhanced by the use of additional fillers. These composite plates are often subjected to dynamic loading conditions which necessitate the study of their static and dynamic behavior. In this study, laminated composite plates (LCP) are fabricated by open layup process with epoxy as a base resin, E-glass fiber as reinforcement, and fillers: flyash and graphene. The fillers are included in order to improve the mechanical properties of the composite. The filler content in the composite is limited to 5% of the total volume. The weight percentage of fiber combined with fillers, treated as reinforcing constituents is limited to 60%. Graphene and flyash are added in different proportions to develop different kinds of LCPs. The free and forced vibrations of LCPs (using simple support end conditions) are measured by an indigenously developed low-cost vibration testing module. The experimental results have been used to validate the results obtained from the mathematical modeling by using fifth-order shear deformation theory and finite element approaches. Additionally, the effect of existing discontinuity in the LCP is studied. Circular holes of different dimensions at different locations are simulated in the numerical model and the consequences on modal frequencies are analyzed.

A Simple Higher-Order Theory for Laminated Composite Plates

1984 ◽  
Vol 51 (4) ◽  
pp. 745-752 ◽  
Author(s):  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
First Order ◽  
First Order Theory

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano [6], but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

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