scholarly journals Use of Polynomial Shape Function in Shear Deformation Theory for Thick Plate Analysis

2016 ◽  
Vol 06 (06) ◽  
pp. 08-20 ◽  
Author(s):  
Ibearugbulem, Owus M
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Thick Plate ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Plate Analysis

scholarly journals Application of alternative II theory to vibration and stability analysis of thick rectangular plates (Isotropic and orthotropic)

2020 ◽  
Vol 39 (1) ◽  
pp. 52-62
Author(s):  
O.M. Ibearugbulem ◽  
S.I. Ebirim ◽  
U.C. Anya ◽  
L.O. Ettu
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequency ◽  
Deformation Theory ◽  
Thick Plate ◽  
Shape Function ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
First Order ◽  
Fundamental Natural Frequency

This work analysed the free vibration and stability of thick isotropic and orthotropic plates with SSSS and SSFS support conditions by applying the alternative II theory based on polynomial shape function. The total potential energy which was obtained by combining the strain energy and external work was reduced to three governing equations using Ritz method. Polynomial shape function which varies with Poisson’s ratio was substituted into the governing equation to obtain the fundamental natural frequency, linear frequency and critical buckling load. The values of frequencies of the first mode and critical loads obtained were compared with those obtained using first order shear deformation theory. For span depth ratio of 10, the fundamental linear frequency for orthotropic SSFS plate corresponding to modulus of elasticity ratios (E1/E2) of 10, 25 and 40 are 0.00156, 0.00219 and 0.00255Hz. The corresponding values using first order shear deformation theory are 0.00152, 0.00212 and 0.00245Hz. Keywords: Fundamental natural frequency, SSSS plate, SSFS plate, Ritz method, Orthotropic thick plate, Isotropic thick plate, Stability, Free vibration

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

scholarly journals New Shape Function for the Bending Analysis of Functionally Graded Plate

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2381 ◽  
Author(s):  
Dragan Čukanović ◽  
Aleksandar Radaković ◽  
Gordana Bogdanović ◽  
Milivoje Milanović ◽  
Halit Redžović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shape Function ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Transverse Load ◽  
Shape Functions ◽  
Bending Analysis ◽  
Pasternak Elastic Foundation

The bending analysis of thick and moderately thick functionally graded square and rectangular plates as well as plates on Winkler–Pasternak elastic foundation subjected to sinusoidal transverse load is presented in this paper. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. This paper presents the methodology of the application of the high order shear deformation theory based on the shape functions. A new shape function has been developed and the obtained results are compared to the results obtained with 13 different shape functions presented in the literature. Also, the validity and accuracy of the developed theory was verified by comparing those results with the results obtained using the third order shear deformation theory and 3D theories. In order to determine the procedure for the analysis and the prediction of behavior of functionally graded plates, the new program code in the software package MATLAB has been developed based on the theories studied in this paper. The effects of transversal shear deformation, side-to-thickness ratio, and volume fraction distributions are studied and appropriate conclusions are given.

scholarly journals Analytical Study of Bending Characteristics of an Elastic Rectangular Plate using Direct Variational Energy Approach with Trigonometric Function

2021 ◽  
Vol 5 (6) ◽  
pp. 916-928
Author(s):  
F. C. Onyeka ◽  
B. O. Mama
Keyword(s):  
Deformation Theory ◽  
Thick Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Total Potential ◽  
Plate Analysis ◽  
Potential Energy Functional

In this paper, an analytical three-dimensional (3D) bending characteristic of an isotropic rectangular thick plate with all edges simply supported (SSSS) and carrying uniformly distributed transverse load using the energy technique is presented. The three-dimensional constitutive relations which involves six stress components were used in the established, refined shear deformation theory to obtain a total potential energy functional. This theory obviates application of the shear correction factors for the solution to the problem. The governing equation of a thick plate was obtained by minimizing the total potential energy functional with respect to the out of plane displacement. The deflection functions which are in form of trigonometric were obtained as the solution of the governing equation. These deflection functions which are the product of the coefficient of deflection and shape function of the plate were substituted back into the energy functional, thereafter a realistic formula for calculating the deflection and stresses were obtained through minimizations with respect to the rotations and deflection coefficients. The values of the deflections and stresses obtained herein were tabulated and compared with those of previous 3D plate theory, refined plate theories and, classical plate theory (CPT) accordingly. It was observed that the result obtained herein varied more with those of CPT and RPT by 25.39% and 21.09% for all span-to-thickness ratios respectively. Meanwhile, the recorded percentage differences are as close as 7.17% for all span-to-thickness ratios, when compared with three dimensional plate analysis. This showed that exact 3D plate theory is more reliable than the shear deformation theory which are quite coarse for thick plate analysis. Doi: 10.28991/esj-2021-01320 Full Text: PDF

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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