Mechanics of Smart Magneto-electro-elastic Nanostructures provides mathematical models for buckling and vibration analysis of flexoelectric and magneto-electro-elastic nanostructures under thermal environment effects. Analytical results are presented in each chapter based on changes in different parameters, including various electric and magnetic potential, non-local parameters or different boundary conditions and their effects on vibration and buckling behavior on nanobeams and nanoplates. Key characteristics of smart materials and their response to external factors are presented, including size-dependency of nanostructures, effect of various gradient indexes, thermal environment effects, and effects of elastic foundation. Reviews vibration and buckling models of the responses of smart magneto-electro-elastic materials Addresses thermal environment and elastic foundation effects of magneto-electro-elastic materials Introduces piezoelectricity, flexoelectricity and magneto-electro-elasticity