On the Boundary Value Problems of Bending of Thin Elastic Plates With Surface Effects

Abstract

We modify classical thin plate theory by incorporating surface effects via the Gurtin–Murdoch surface model to accommodate the mechanical behavior of thin plates at the nanoscale. We formulate the corresponding Dirichlet and Neumann boundary value problems and establish uniqueness results in the appropriate function spaces. In addition, we obtain the fundamental solution of the governing system of equations, which is central to further studies concerning well-posedness analysis of the model by the boundary integral equation method. Finally, we validate our model by comparison with results in the existing literature.