Nonlinear statics of magneto-electro-elastic nanoplates considering flexomagnetoelectric effect based on nonlocal strain gradient theory

Abstract

The nonlinear static behavior of hygrothermal magnetoelectroelastic(MEE) nanoplates considering the flexomagnetoelectric (FME) effect is researched by engaging the first-order shear deformation theory (FSDT). The constitutive equations of MEE nanoplates take into account the FME effect and hygrothermal effect. Leveraging the FSDT, von Karman's nonlinear equation and Hamilton's principle, the nonlinear control equation for hygrothermal MEE nanoplates can be derived by using the variational approach. The nonlocal strain gradient theory (NSGT) has application in the size effect of MEE nanoplates. The nonlocal nonlinear term in the control equation is handled by employing the Airy stress function, and then the non-linear mechanical model is solved by the Galerkin method. Thus, the nonlinear load-deflection curves (NLDC) of the MEE nanoplate are obtained via the introduction of material parameters, enabling an examination of the impact of various factors such as the FME effect, two small size parameters of NSGT and other parameters on the nonlinear bending behavior of MEE nanoplates. In conclusion, this study offers a theoretical foundation for taking into account the FME effect in the development of nanodevices, thereby contributing to advancements in this field.