Thermal buckling of magneto-electric functionally graded curved-nanosized beam using nonlocal strain gradient theory and sinusoidal beam model including transverse normal deformation

This study concerns the thermal buckling characteristics of size-dependent Magneto-Electro-Elastic (MEE) Functionally Graded (FG) curved nanobeams. The formulation makes use of a nonlocal strain-gradient approach and a higher-order beam model based on sinusoidal theory, combined with the beam thickness stretching effect. Functionally graded material comprising metal and ceramic is considered for the beam structure to produce the desired variation in electrical, magnetic, and thermoelastic properties. The equilibrium equations formed using Hamilton’s principle are general and applicable to static/dynamic analysis and are solved analytically by employing Navier’s solutions. The thermal buckling temperatures predicted here are firstly validated against the available flat beams results under FG and Electro-Magnetic (EM) environments. A parametric study is carried out involving the nonlocal stress and material length-scale parameters, and assuming other design variables of the curved structure, material power-law index, electrical, magnetic and elastic coupling and externally applied electrical and magnetic fields on the thermo-elastic stability of the EM curved nanobeam.