On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Abstract

By relying on the Euler–Bernoulli beam model and energy variational formula, we indicate critical temperature causes in the buckling of piezo-flexomagnetic microscale beams. The corresponding size-dependent approach is underlying as a second strain gradient theory. Small deformations of elastic solids are assessed, and the mathematical discussion is linear. Regardless of the pyromagnetic effects, the thermal loading of the thermal environment varies in three states along with the thickness, which is linear, uniform, and parabolic forms. We then establish the results by developing consistent shape functions that independently evaluate boundary conditions. Next, we analytically develop and explore the effective properties of the studied beam concerning vital factors. It was achieved that piezomagnetic-flexomagnetic microbeams are more affected by the thermal environment while the thermal loading is parabolically distributed across the thickness, particularly when the boundaries involve simple supports.

Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect

“…On the other hand, atoms consist of a large strain gradient on a small scale. This is mathematically simulated by the strain gradient elasticity theory of Mindlin [73]. These two phenomena are unified, called nonlocal strain gradient elasticity theory [83], by which a small scale is transferred into a continuum media based on a differential model.…”

“…The conclusions included in this paper are very significant in the field of nanostructures. Malikan et al [73] presented the nanobeam with porous state and piezo-flexomagnetic effect and the impact of beam size. Obtained results show that the flexomagnetic effect of the structure is dependent on the porosity of the materials.…”

A novel numerical approach for the stability of nanobeam exposed to hygro‐thermo‐magnetic environment embedded in elastic foundation

“…The axial stability and bifurcation point of a functionally graded piezomagnetic structure, including flexomagneticity in a thermal environment, are addressed by Malikan et al [17] using the Galerkin weighted residual method and Timoshenko beam theory. Based on thin beam theory, Malikan et al [18] conducted an investigation on piezomagnetic-flexomagnetic micro-size beam-shaped sensors where the microstructural effect was investigated using the strain gradient theory. In a pioneering work, Malikan et al [19] studied the instabilities and post buckling of piezomagnetic and flexomagnetic nanostructures using Euler-Bernoulli beam theory and nonlocal strain gradient elasticity theory.…”

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

“…The classical continuum theory cannot capture the impact of small scale, and therefore, the mechanical behavior of micro/nanostructures cannot be appropriately predicted. Therefore, non-classical continuum theories have been generalized to include the features of micro-and nanomaterials, for instance, the strain gradient theory [35,36], classical couple stress model, non-local elasticity and the modified couple stress theories [37,38].…”