Existence of solution in the bending of thin plates with Gurtin–Murdoch surface elasticity

Abstract

We consider the well-posedness of classical boundary value problems in a theory of bending of thin plates which incorporates the effects of surface elasticity via the Gurtin–Murdoch surface model. We employ the fundamental solution of the governing system of equations to develop integral-type solutions of the corresponding Dirichlet, Neumann, and Robin boundary value problems. Using the boundary integral equation method, we subsequently establish results for the existence of a solution in the appropriate function spaces.

The influence of surface effects on axisymmetric vibration of graded porous Mindlin circular nanoplate in a temperature field

“…It is introducing Equations ( 22), ( 23), ( 24), (25), and (26) into Equations ( 41) and ( 42) and assuming that the FG porous circular nanoplate experiences simple harmonic response vibration, so that 𝑤(𝑟, 𝑡) = w(𝑟) cos Ω𝑡, 𝜓(𝑟, 𝑡) = ψ(𝑟) cos Ω𝑡, where w(𝑟), ψ(𝑟) represent the shape functions and Ω is its natural frequency, a set of displacement-type governing equations of motion of the problem in temperature field are obtained as follows.…”

“…With the help of this definition, true nanoparticles and their surfaces have unique elastic properties and residual stresses. Recently, Gharahi and Schiavone [25] analyzed the existence of a solution in the bending of nanoplate with gurtin‐murdoch surface elasticity. The nanostructures mentioned in the above literature are all made of uniform nanomaterials.…”