Analytical solution for functionally graded plate on elastic foundation using Mindlin and Kirchhoff model based on a modified couple stress theory

In the present research, buckling and vibration of functionally graded plate on elastic foundation using Mindlin and Kirchhoff model based on a modified couple stress theory are discuss. The present pattern own one material length scale parameter and can obtain the size effect two-constituent material variation through the plate thickness. The equations of motion are derived using Hamilton’s principle. Analytical solutions for buckling and vibration of a simply supported plate are presented to bring out the result of the substance length scale parameter on the buckling, and vibration replication of microplates. ,the newly developed plate models can be used to capture the size effects in functionally graded nanoplates.