Thermal buckling and vibration of functionally graded sinusoidal microbeams incorporating nonlinear temperature distribution using DQM

2016 ◽  
Vol 40 (6) ◽  
pp. 665-689 ◽  
Author(s):  
Jian Lei ◽  
Yuming He ◽  
Song Guo ◽  
Zhenkun Li ◽  
Dabiao Liu
Keyword(s):  
Temperature Distribution ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Nonlinear Temperature

scholarly journals Thermal buckling of imperfect functionally graded cylindrical shells according to Wan-Donnell model

2008 ◽  
Vol 30 (3) ◽  
Author(s):  
Hoang Van Tung ◽  
Nguyen Dinh Duc
Keyword(s):  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Form Solution ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Thermal Loads ◽  
Geometrical Imperfection ◽  
Graded Material ◽  
Nonlinear Temperature ◽  
Power Law Index

A thermal buckling analysis of imperfect circular cylindrical shells of functionally graded material is considered. The material properties are assumed varying as a power form of thickness coordinate variable. The Donnell equilibrium and stability equations are considered and the Wan-Donnell model for initial geometrical imperfection is adopted. The thermal loads include the uniform temperature rise and nonlinear temperature change across the thickness of shell. A closed form solution for the thermal buckling of simply supported cylindrical FG shell under the described thermal loads is obtained. The influences of the relative thickness, the imperfection size and the power law index on buckling thermal loads are all discussed.

Thermal Buckling Analysis of Circular FGP with Actuator/Actuator Piezoelectric Layers Based on Neutral Plane Method

2012 ◽  
Vol 29 (1) ◽  
pp. 157-167 ◽  
Author(s):  
M. M. Najafizadeh ◽  
M. Malmorad ◽  
A. Sharifi ◽  
A. Joodaky
Keyword(s):  
Thermal Loading ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Neutral Plane ◽  
Functionally Graded Plates ◽  
Temperature Changes ◽  
First Order ◽  
Piezoelectric Layers ◽  
Nonlinear Temperature

AbstractIn this research, thermal buckling analysis of circular functionally graded plates with Actuator/Actuator piezoelectric layers (FGPs) is studied based on neutral plane, classical and first order shear deformation plate theories. Mechanical properties of the plate are considered as those of Reddy Model. Plate is assumed to be under thermal loading. Nonlinear temperature rises through the thickness and boundary conditions are considered clamped. Equilibrium and stability equations have been derived using calculus of variations and application of Euler equations. Finally, critical buckling temperature changes are studied based on the mentioned theories for a sample plate. An appropriate agreement is seen among the present results and the results of other researches.

A study on thermal buckling load of clamped functionally graded beams under linear and nonlinear thermal gradient across thickness

2016 ◽  
Vol 232 (9) ◽  
pp. 769-784 ◽  
Author(s):  
Aritra Majumdar ◽  
Debabrata Das
Keyword(s):  
Stainless Steel ◽  
Temperature Distribution ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Mathematical Formulation ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Linear Temperature ◽  
Buckling Loads ◽  
Finite Element Software

The present work aims at the determination of thermal buckling loads of various functionally graded material beams with both ends clamped. Thermal loading is applied by applying linear temperature distribution and nonlinear temperature distribution at steady state heat conduction condition, across the beam thickness. Temperature dependences of the material properties, considered in the formulation, make the present problem physically nonlinear. Also, the effect of limit thermal load at which the effective elastic modulus and/or thermal expansion coefficient become theoretically zero is considered. The mathematical formulation is based on Euler–Bernoulli beam theory. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The solution of the governing equation is obtained using an iterative method. The validation of the present work is carried out with the available results in the literature and with the results generated by finite element software ANSYS. Four different functionally materials are considered, namely, stainless steel/silicon nitride, stainless steel/alumina, stainless steel/zirconia, and titanium alloy/zirconia. Comparative results are presented to show the effects of variations of volume fraction index, length–thickness ratio, and material constituents on nondimensional thermal buckling loads.

Thermal Buckling of Functionally Graded Sandwich Beams

2019 ◽  
Vol 1156 ◽  
pp. 43-59 ◽  
Author(s):  
Ahmed Amine Daikh ◽  
Mohamed Guerroudj ◽  
Mohamed El Adjrami ◽  
Abdelkader Megueni
Keyword(s):  
Thermal Loading ◽  
Beam Theory ◽  
Form Solution ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Sigmoid Function ◽  
Sandwich Beams ◽  
Nonlinear Temperature ◽  
Inhomogeneity Parameter ◽  
Nonlinear Distribution

Thermal buckling of new model of functionally graded (FG) sandwich beams is presented in this study. Material properties and thermal expansion coefficient of FG sheets are assumed to vary continuously along the thickness according to either power-law (P-FGM) or sigmoid function (S-FGM) in terms of the volume fractions of the constituents. Equations of stability are derived based on the generalized higher-order shear deformation beam theory. Thermal loads are supposed to be constant, linear or nonlinear distribution along the thickness direction. An accurate form solution for nonlinear temperature variation through the thickness of S-FGM and P-FGM sandwich beams is presented. Numerical examples are presented to examine the influence of thickness ratio, the inhomogeneity parameter and the thermal loading kinds on the thermal buckling response of various types of FG sandwich beams.

scholarly journals A new boundary element algorithm for modeling and simulation of nonlinear thermal stresses in micropolar FGA composites with temperature-dependent properties

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Modeling And Simulation ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Computation Time ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Time Step ◽  
Kirchhoff Transformation ◽  
Nonlinear Temperature ◽  
Temperature Dependent Properties

AbstractThe main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the Cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.

scholarly journals Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

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