Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element

2020 ◽  
pp. 113309
Author(s):  
Cong Ich Le ◽  
Ngoc Anh T. Le ◽  
Dinh Kien Nguyen
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Third Order

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

2019 ◽  
Vol 50 (9-11) ◽  
pp. 267-290
Author(s):  
Ali Bakhsheshy ◽  
Hossein Mahbadi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Scale Parameter ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
The Third

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment

2012 ◽  
Vol 226 (12) ◽  
pp. 2860-2873 ◽  
Author(s):  
AR Setoodeh ◽  
M Ghorbanzadeh ◽  
P Malekzadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Thermal Environment ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Sandwich Beams ◽  
Two Dimensional

In this article, free vibration analysis of elastically supported sandwich beams with functionally graded face sheets subjected to thermal environment is presented. In order to accurately include the transverse shear deformation and the inertia effects, two-dimensional elasticity theory is used to formulate the problem. The layerwise theory in conjunction with the differential quadrature method is employed to discretize the governing equations in the thickness and axial directions, respectively. The material properties of functionally graded face sheets are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution. For the purpose of comparison, the problem under consideration is also solved using two-dimensional finite element method and the first-order shear deformation theory. The accuracy, convergence, and versatility of the method are demonstrated by comparing the results with those of the two aforementioned approaches and also with the existing solutions in literature. Eventually, some new numerical results are presented which depict the effects of different material and geometrical parameters on natural frequencies and mode shapes of the beam.

scholarly journals A NEW C0 THIRD-ORDER SHEAR DEFORMATION THEORY FOR THE NONLINEAR FREE VIBRATION ANALYSIS OF STIFFENED FUNCTIONALLY GRADED PLATES

2021 ◽  
Vol 19 (2) ◽  
pp. 285
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Nonlinear Free Vibration ◽  
Third Order

Nonlinear free vibration of stiffened functionally graded plates is presented by using the finite element method based on the new C0 third-order shear deformation theory. The material properties are assumed to be graded in the thickness direction by a power-law distribution. Based on the Von Karman theory and the third-order shear deformation theory, the nonlinear governing equations of motion are derived from the Hamilton’s principle. An iterative procedure based on the Newton-Raphson method is employed in computing the natural frequencies and mode shape. The comparison between these solutions and the other available ones suggests that this procedure is characterized by accuracy and efficiency.

scholarly journals Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory

2016 ◽  
Vol 38 (2) ◽  
pp. 103-122 ◽  
Author(s):  
Pham Tien Dat ◽  
Do Van Thom ◽  
Doan Trac Luat
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Power Law Distribution ◽  
Third Order ◽  
The Third

In this paper, the free vibration of functionally  sandwich grades plates with stiffeners is investigated by using the finite  element method. The material properties are assumed to be graded in the  thickness direction by a power-law distribution. Based on the third-order  shear deformation theory, the governing equations of motion are derived from  the Hamilton's principle. A parametric study is carried out to highlight the  effect of material distribution, stiffener parameters on the free  vibration characteristics of the plates.

scholarly journals Free Vibration Frequency of Thick FGM Spherical Shells Based on a Third-order Shear Deformation Theory

2020 ◽  
Vol 13 (4) ◽  
pp. 766-778
Author(s):  
Mohammad Zannon ◽  
Abdullah Abu-Rqayiq ◽  
Ammar Al-bdour
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Spherical Shells ◽  
Free Vibration Frequency ◽  
Vibration Problems

In this paper, we consider free vibration problems of functionally graded thick spherical shells. The analysis performs by collecting the radial basis functions, according to the Third Order Shear Deformation Theory that accounts for through the thickness deformation using the principle of virtual work. Numerical results include spherical shell panels with all edges clamped or simply supported to demonstrate the accuracy of the present approach.

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