Differential cubature method for gradient-elastic Kirchhoff plates

In this article, the differential cubature method is applied for the problem describing the static deformations of gradient-elastic Kirchhoff plates. The theory of gradient elasticity applied for the Kirchhoff plate model results in a sixth order partial differential equation with a set of corresponding boundary conditions. The differential cubature method is shown to be able to solve the problem with a relatively small number of grid points and with a small computational effort. In particular, the correct qualitative dependence of the solution on the size effect parameter is encountered. However, it is demonstrated that the differential cubature method possesses certain deficiencies related to the resulting system matrices and enforcement of boundary conditions, which is an issue that, surprisingly, has not been studied thoroughly before.

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