In the present work, closed-form solutions for the linear and nonlinear stability of the magnetoelectric nanoplate strips consisting of piezo-flexoelectric and piezo-flexomagnetic layers are presented. In the framework of the nonlocal strain gradient and first-order shear deformation theories, magneto-electro-mechanical responses are obtained for simply supported and clamped end conditions. Excellent agreements are observed between the obtained results and the existing literature. The effect of several parameters on critical buckling load and post-buckling path is investigated. Our outcomes reveal that the post-buckling load-carrying capacity increases considerably in the case of a double-layer ME nano-plate strip compared to a single-layer (piezo-flexoelectric and piezo-flexomagnetic) with the same thickness and length. Further, the post-buckling deformation decreases with a decrease in initial electric voltage and an increase in initial magnetic potential. The closed-form solutions and numerical results of this work are useful for future analyses and the design of such nanostructures.

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