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Thermal buckling and free vibration of Euler–Bernoulli FG nanobeams based on the higher-order nonlocal strain gradient theory

Janevski G., Despenić N., Pavlović I.

Archives of Mechanics

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2020

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Vol. 72, nr 2

139--168

EN

A size-dependent Euler–Bernoulli beam model is derived within the framework of the higher-order nonlocal strain gradient theory. Nonlocal equations of motion are derived by applying Hamilton’s principle and solved with an analytical solution. The solution is obtained using the Navier solution procedure. In the case of simply supported boundary conditions, the analytical solutions of natural frequencies and critical buckling temperature for free vibration problems are obtained. The paper investigates the thermal effects on buckling and free vibrational characteristics of functionally graded size-dependent nanobeams subjected to various types of thermal loading. The influence of higher-order and lower-order nonlocal parameters and strain gradient scale on buckling and vibration are investigated for various thermal conditions. The obtained results are compared with previous research.

2

Thermal buckling of temperature-dependent functionally graded Timoshenko beams

Chen Wei-Ren, Chen Chun-Sheng, Chang Heng

Archive of Mechanical Engineering

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2019

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Vol. LXVI, nr 4

393--415

EN

Thermal buckling behavior of a functionally graded material (FGM) Timoshenko beam is studied based on the transformed-section method. The material and thermal properties of the FGM beam are assumed to vary across the beam thickness according to a power-law function, a sigmoid function and an exponential function. The results of buckling temperature for the FGM beams with respective temperature-dependent and temperature-independent properties under uniform and non-linear temperature rises are presented. Some results are compared with those in the published literature to verify the accuracy of the present work. The effects of the material distributions, temperature fields, temperature-dependent properties and slenderness ratios on the thermal buckling behaviors of FGM beams are discussed. It is believed that the present model provides engineers with a simple and effective method to study the effects of various parameters of the FGM beam on its thermal buckling behavior.

3

Three-dimensional thermal buckling analysis of functionally graded cylindrical panels using differential quadrature method (DQM)

Ahmadi S. A., Pourshahsavari H.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 1

135--147

EN

Thermal buckling analysis of functionally graded cylindrical panels subjected to various conditions is discussed in this paper. Buckling governing equations are solved using the differential quadrature method. It is assumed that the mechanical properties of the panel are graded through thickness according to a power function of the thickness variable. The panel is assumed to be under the action of three types of thermal loading including uniform temperature rise and variable temperature rise in the axial and radial direction. In the present study, the effects of power law index, panel angle, different thermal load conditions and geometric parameters on the buckling behavior of functionally graded curved panels are studied. The results obtained through the present method are compared to the finite element solutions and the reported results in the literature. A desirable compatibility is concluded.

4

Buckling of heated temperature dependent FGM cylindrical shell surrounded by elastic medium

Sabzikar Boroujerdy M, Naj R, Kiani Y

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 4

869--881

EN

Based on the Donnell theory of shells combined with the von-Karman type of geometrical nonlinearity, three coupled equilibrium equations for a through-the-thickness functionally graded cylindrical shell embedded in a two parameter Pasternak elastic foundation are ob- tained. Equivalent properties of the shell are obtained based on the Voigt rule of mixture in terms of a power law volume fraction for the constituents. Properties of the constituents are considered to be temperature dependent. The temperature profile through the shell thick- ness is obtained by means of the central finite difference method. Linear prebuckling analysis is performed to obtain the prebuckling forces of the cylindrical shell. Stability equations are derived based on the well-known adjacent equilibrium criterion. Three coupled partial dif- ferential stability equations are solved with the aid of a hybrid Fourier-GDQ method. After validating the numerical results, some parametric studies are conducted to investigate the influence of various parameters, especially foundation interaction. It is shown that elastic foundation enhances the critical buckling temperature difference of the shell and violates the buckled pattern.