A Comparison between Thermal Buckling Solutions of Power-Law, Sigmoid, Exponential FGM Circular Plates

Khorshidv, A. R.; Eslami, M. R.

doi:10.7763/ijet.2013.v5.539

Cited by 7 publications

(3 citation statements)

References 8 publications

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“…First-order shear deformation theories and different higher-order shear deformation theories were used to study FGM plates [30,31]. Under clamped boundary circumstances for material attribute modification by a power law, sigmoid law, and exponential rule, researchers examined the FGM circular plate [32,33]. The free and forced vibration of a sigmoid FGM plate on an elastic basis was studied by using a higher-order shear deformation theory [33].…”

Section: Introductionmentioning

confidence: 99%

Computational modeling of sigmoid functionally graded material (SFGM) plate

Sharma

Kumar

et al. 2023

Mater. Res. Express

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The first-order shear deformation theory (FSDT) was used to explore the natural frequency response of functionally graded piezoelectric plates subjected to static electrical and mechanical strain in this present study. A monomorph model for a functionally graded piezoelectric plate with material properties that change according to sigmoid law with respect to plate thickness has been considered. A three-dimensional finite element model with a free tetrahedral element mesh was created using COMSOL 4.2 Multiphysics® software, with each node having three degrees of freedom. Variations in the FGPM plate's free vibration boundary conditions, composition, and geometry have all been investigated. In free vibration analysis, non-dimensional natural frequency of FGPM plate initially decreasing considerably and then remaining almost constant with the increase in volume fraction index when material property graded by power law. When material properties are varied by sigmoid law, with an increase in volume fraction index, the non-dimensional natural frequency of FGPM plates remains virtually constant. FGPM plates have a lower non-dimensional natural frequency if the thickness to width ratio is greater. Non-dimensional natural frequencies of Clamped-Clamped FGPM plates (C-C-C-C) are greater compared to Clamped-Free FGPM (C-F-C-F) and Simply Supported Free FGPM (S-F-S-F).

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Section: Introductionmentioning

confidence: 99%

Computational modeling of sigmoid functionally graded material (SFGM) plate

Sharma

Kumar

et al. 2023

Mater. Res. Express

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“…Many authors have utilized power low (P-FGM), sigmoid law (S-FGM) and exponential law (E-FGM) to get the desired material properties of the FGM plate along the preferred direction. Khorshidv and Eslami (2013) investigated the buckling analysis of P-FGM, S-FGM and E-FGM in the thermal environment. Thermal buckling analysis of rectangular S-FGM plate using FSDT under the uniform, linear and nonlinear temperature rise has been investigated by Atmane et al (2016) and Fekrar et al (2013).…”

Section: Introductionmentioning

confidence: 99%

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

Sah

Ghosh

2021

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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.

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“…Van et al [20,21] introduced a new transverse shear function based on the HSDT and an accurate and effective mesh-free approximation based on the radial point interpolation method, analyzed the nonlinear thermal buckling of FGM plates subjected to various temperature distributions along the thickness, and the post-buckling responses of FGM plates in mechanical edge compression was also analyzed. Khorshidv and Eslami [22] compared and analyzed the effects of power-law, sigmoid and exponential FGM on the thermal buckling behavior of FGM circular plates by employing the CPT. Considering the material and geometric nonlinearity, Moita et al [23] analyzed the nonlinear mechanical behavior of power-law, sigmoid FGM plate-shell type structures using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear axisymmetric thermomechanical response of FGM circular plates

Zhao

2020

J Braz. Soc. Mech. Sci. Eng.

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Based on von Kármán plate theory, axisymmetric geometrically nonlinear governing equations of simple power-law type functionally graded material (FGM) circular plates are derived. Material properties are assumed to be temperature-independent, and thermal or/and mechanical loads are considered in the derivation. Considering clamped boundary conditions, the dimensionless critical (lowest) buckling temperature (temperature difference) 14.684 of the systems is obtained by analyzing linear-eigenvalue problem. With this constant and an analytical formula proposed in this paper, accurate dimensional critical (lowest) buckling temperature (temperature difference) of any specified clamped FGM circular plate can be easily calculated. Moreover, two-point boundary value problem posed by the governing equations and the clamped boundary conditions is solved using the shooting method. Thermal buckling response under thermal load and geometrically nonlinear mechanical behaviors under thermomechanical load of the system are discussed. When the temperature difference of the upper and lower surfaces of FGM plates exists, the solution of one-dimension Fourier heat conduction equation is an infinite series, which depicts a nonlinear temperature field (NLTF) along the thickness direction of plates. The effects of the initial terms of the series on the accuracy of solutions are examined. The results reveal it is necessary to take enough the initial terms of the series even for thinner FGM plates. Typical load-deflection curves of the clamped FGM circular plates with different temperature fields (along the thickness) are presented. For a given temperature field, the clamped FGM circular plates under transverse uniform load are a hard stiffness nonlinear system. When the values of thermal and mechanical load and their loading sequence meet certain combinations, the clamped circular plate will inevitably undergo secondary buckling (snap-through buckling).

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A Comparison between Thermal Buckling Solutions of Power-Law, Sigmoid, Exponential FGM Circular Plates

Abstract: Index Terms-Classical plate theory, thermal buckling, functionally graded material.

Cited by 7 publications

References 8 publications

Computational modeling of sigmoid functionally graded material (SFGM) plate

Computational modeling of sigmoid functionally graded material (SFGM) plate

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

Nonlinear axisymmetric thermomechanical response of FGM circular plates

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