A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings

Abstract

In the present work, the non-linear post-buckling load-deflection behavior of tapered functionally graded material beam is studied for different in-plane thermal loadings. Two different thermal loadings are considered. The first one is due to the uniform temperature rise and the second one is due to the steady-state heat conduction across the beam thickness leading to non-uniform temperature rise. The governing equations are derived using the principle of minimum total potential energy employing Timoshenko beam theory. The solution is obtained by approximating the displacement fields following Ritz method. Geometric non-linearity for large post-buckling behavior is considered using von Kármán type non-linear strain-displacement relationship. Stainless steel/silicon nitride functionally graded material beam is considered with temperature-dependent material properties. The validation of the present work is successfully performed using finite element software ANSYS and using the available result in the literature. The post-buckling load-deflection behavior in non-dimensional plane is presented for different taperness parameters and also for different volume fraction indices. Normalized transverse deflection fields are presented showing the shift of the point of maximum deflection for various deflection levels. The results are new of its kind and establish benchmark for studying non-linear thermo-mechanical behavior of tapered functionally graded material beam.

A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis

“…The total strain energy ( U ) of the beam is given by, U = U ax + U sh + U th , where U ax , U sh and U th denote the strain energies due to normal strain in the axial direction, due to transverse shear strains and due to thermal pre-stress, 36 respectively. The expressions of U ax , U sh and U th are derived as given below…”

Free vibration behavior of tapered functionally graded material beam in thermal environment considering geometric non-linearity, shear deformability and temperature-dependent thermal conductivity

“…The post-buckling equilibrium path for HH beams under both UTR and HC is not furnished in the present work as it is available in the study by Paul and Das. 21

Figure 4.Post-buckling load–deflection path of CC tapered ( n = 0.5) stainless steel/silicon nitride beam with k = 1.0: (a) UTR and (b) HC.

…”

“…The literature review reveals that studies on tapered FGM beams under thermal loading are scarce. To the best knowledge of the authors, the research findings in this regard are available in the studies by Niknam et al 20 and Paul and Das 21 . In the study by Niknam et al, 20 static analysis under UTR based on EBT is reported presenting limited results for deformed configuration of fixed-ended beam.…”

On the vibration analysis of coupled transverse and shear piezoelectric functionally graded porous beams with higher-order theories

“…For detailed static and dynamic investigations of structural members made of FGMs, one may see the literature. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] Various special methods such as chemical and physical deposition, powder stacking, plasma spraying, and sintering have been used to fabricate FGMs. It is recently reported that in production of FGMs, internal porosities may appear inside the material structure due to the huge difference between the solidification temperatures of the material constituents during the sintering process.…”