scholarly journals Strong and Weak Formulations of a Mixed Higher-Order Shear Deformation Theory for the Static Analysis of Functionally Graded Beams under Thermo-Mechanical Loads

2020 ◽  
Vol 4 (4) ◽  
pp. 158 ◽  
Author(s):  
Chih-Ping Wu ◽  
Zhan-Rong Xu
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Static Analysis ◽  
Material Properties ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mechanical Loads ◽  
Effective Material Properties ◽  
Fg Beam

The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the FG beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

Computational Development of a 4-Unknowns Trigonometric Quasi-3D Shear Deformation Theory to Study Advanced Sandwich Plates and Shells

2016 ◽  
Vol 08 (04) ◽  
pp. 1650049 ◽  
Author(s):  
J. L. Mantari
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Sandwich Plates And Shells ◽  
Plates And Shells ◽  
First Time ◽  
Stretching Effect

In this paper, a simple and accurate sinusoidal trigonometric theory (STT) for the bending analysis of functionally graded single-layer and sandwich plates and shells is presented for the first time. The principal feature of this theory is that models the thickness stretching effect with only 4-unknowns, even less than the first order shear deformation theory (FSDT) which as it is well-known has 5-unknowns. The governing equations and boundary conditions are derived by employing the principle of virtual work. Then, a Navier-type closed-form solution is obtained for functionally graded plates and shells subjected to bi-sinusoidal load for simply supported boundary conditions. Consequently, numerical results of the present STT are compared with other refined theories, FSDT, and 3D solutions. Finally, it can be concluded that: (a) An accurate but simple 4-unknown STT with thickness stretching effect is developed for the first time. (b) Optimization procedure (described in the paper) appear to be of paramount importance for 4-unknown higher order shear deformation theories (HSDTs) of this gender, so deserves a lot of further research. (c) Transverse shear stresses results are sensitive to the theory and need carefully attention.

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 A General Ritz Algorithm for Static Analysis of Arbitrary Laminated Composite Plates using First Order Shear Deformation Theory

2013 ◽  
Vol 10 (2) ◽  
pp. 1 ◽  
Author(s):  
RF Rango ◽  
FJ Bellomo ◽  
LG Nallim
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Static Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
General Algorithm ◽  
Laminated Composite Plates ◽  
First Order

 This paper is concerned with the bending of laminated composite plates with arbitrary lay-up and general boundary conditions. The analysis is based on the small deflection, first-order shear deformation theory of composite plates, which utilizes the Reissner-Mindlin plate theory. In solving the aforementioned plate problems, a general algorithm based on the Ritz method and the use of beam orthogonal polynomials as coordinate functions is derived. This general algorithm provides an analytical approximate solution that can be applied to the static analysis of moderately thick laminated composite plates with any lamination scheme and combination of edge conditions. The convergence, accuracy, and flexibility of the obtained general algorithm are shown by computing several numerical examples and comparing some of them with results given in the literature. Some results, including general laminates and nonsymmetrical boundary conditions with free edges, are also presented. 

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