Thermal buckling behavior of power and sigmoid functionally graded material sandwich plates using nonpolynomial shear deformation theories

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Supen Kumar Sah ◽  
Anup Ghosh
Keyword(s):  
Shear Deformation ◽  
Temperature Variation ◽  
Temperature Rise ◽  
Sandwich Plate ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Sandwich Plates ◽  
Content Type ◽  
Shear Deformation Theories ◽  
Sinusoidal Temperature

PurposeThe purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.Design/methodology/approachThermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.FindingsCritical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.Originality/valueThe temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

A new simple shear deformation theory for free vibration analysis of isotropic and FG plates under different boundary conditions

2015 ◽  
Vol 11 (3) ◽  
pp. 437-470 ◽  
Author(s):  
Amale Mahi ◽  
El Abbas Adda Bedia ◽  
Abdelouahed Tounsi ◽  
Amina Benkhedda
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Temperature Rise ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Content Type ◽  
Different Boundary Conditions ◽  
Fg Plates ◽  
Shear Deformation Theories

Purpose – A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues. Design/methodology/approach – Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions. Findings – In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems. Originality/value – To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.

Assessment of higher order transverse shear deformation theories for modeling and buckling analysis of FGM plates using RBF based meshless approach

2018 ◽  
Vol 14 (5) ◽  
pp. 891-907 ◽  
Author(s):  
Rahul Kumar ◽  
Jeeoot Singh
Keyword(s):  
Shear Deformation ◽  
Design Methodology ◽  
Buckling Analysis ◽  
Thin Plates ◽  
Buckling Loads ◽  
Thick Plates ◽  
Content Type ◽  
Matlab Code ◽  
Shear Deformation Theories ◽  
Good Agreement

Purpose The purpose of this paper is to assess different five variables shear deformation plate theories for the buckling analysis of FGM plates. Design/methodology/approach Governing differential equations (GDEs) of the theories are derived by employing the Hamilton Principle. A polynomial radial basis function (RBF)-based Meshless method is used to discretize the GDEs, and a MATLAB code is developed to solve these discretize equations. Findings Numerical results are obtained for buckling loads. The results are compared with other available results for validation purpose. The effect of the span-to-thickness ratio and grading index is observed. It is observed that some theories underpredict the deflection for thick plates, while at the same time they seem to be in good agreement with other theories for thin plates. Originality/value This paper assesses the different theories with the same method to determine their applicability.

A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates

2011 ◽  
Vol 14 (1) ◽  
pp. 5-33 ◽  
Author(s):  
Mohamed Bourada ◽  
Abdelouahed Tounsi ◽  
Mohammed Sid Ahmed Houari ◽  
El Abbes Adda Bedia
Keyword(s):  
Plate Theory ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Plate Theory

Bending analysis of functionally graded sandwich plates using the refined finite strip method

2021 ◽  
pp. 109963622110204
Author(s):  
Mohammad Naghavi ◽  
Saeid Sarrami-Foroushani ◽  
Fatemeh Azhari
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Finite Strip ◽  
Strip Method ◽  
Finite Strip Method

In this study, static analysis of functionally graded (FG) sandwich plates is performed using the finite strip method based on the refined plate theory (RPT). Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. Differential equations of FG sandwich plates are obtained using Hamilton's principle and stiffness and force matrices are formed using the finite strip method. The central deflection and the normal stress values are obtained for a sinusoidal loaded FG sandwich plate and the accuracy of the results are verified against those obtained from other theories such as the classical plate theory (CPT), the first-order shear deformation theory (FSDT), and the higher order shear deformation theory (HSDT). For the first time, this study presents a finite strip formulation in conjunction with the RPT to analyze FG Sandwich plates. While the proposed method is fast and simple, it is capable of modeling a variety of boundary conditions.

scholarly journals THERMAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR PLATE RESTING ON THE PASTERNAK ELASTIC FOUNDATION VIA THE DIFFERENTIAL TRANSFORM METHOD

2017 ◽  
Vol 15 (3) ◽  
pp. 545 ◽  
Author(s):  
Fatemeh Farhatnia ◽  
Mahsa Ghanbari-Mobarakeh ◽  
Saeid Rasouli-Jazi ◽  
Soheil Oveissi
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Temperature Rise ◽  
Volume Fraction ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transform Method ◽  
Pasternak Elastic Foundation ◽  
Differential Transform

In this paper, we propose a thermal buckling analysis of a functionally graded (FG) circular plate exhibiting polar orthotropic characteristics and resting on the Pasternak elastic foundation. The plate is assumed to be exposed to two kinds of thermal loads, namely, uniform temperature rise and linear temperature rise through thickness. The FG properties are assumed to vary continuously in the direction of thickness according to the simple power law model in terms of the volume fraction of two constituents. The governing equilibrium equations in buckling are based on the Von-Karman nonlinearity. To obtain the critical buckling temperature, we exploit a semi-numerical technique called differential transform method (DTM). This method provides fast accurate results and has a short computational calculation compared with the Taylor expansion method. Furthermore, some numerical examples are provided to consider the influence of various parameters such as volume fraction index, thickness-to-radius ratio, elastic foundation stiffness, modulus ratio of orthotropic materials and influence of boundary conditions. In order to predict the critical buckling temperature, it is observed that the critical temperature can be easily adjusted by appropriate variation of elastic foundation parameters and gradient index of FG material. Finally, the numerical results are compared with those available in the literature to confirm the accuracy and reliability of the DTM to determine the critical buckling temperature.

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