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

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.