We consider the symmetric formulation of the interior penalty discontinuous Galerkin finite element method for the numerical solution of the biharmonic equation with Dirichlet boundary conditions in a bounded polyhedral domain in R, d ≥ 2. For a shape-regular family of meshes ? Partially supported by CNPq Brazil ?? Grant from CNPq Brazil Correspondence to: Endre Süli 2 Igor Mozolevski et al. co...

The classical Euler–Bernoulli beam model and Kirchhoff plate are very useful on the macroscopic scale. In context of Eringen’s nonlocal elasticity theory, this article aims to develop criteria applicability nanoscale models based Timoshenko Mindlin via wave propagation theory. corresponding governing differential equations for derived by Hamilton’s principle, dispersion then obtained. By applyi...

Nonlinear vibration and postbuckling behavior of a single layer graphene sheet (SLGS) embedded in a polymer matrix aroused by the nonlinear van der Waals (vdW) forces are investigated using the Kirchhoff plate theory. The interfacial vdW forces are described by a nonlinear function in terms of the graphene deflection. Through harmonic balance method, the nonlinear relation between deflection am...

The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acou...

Positivity preserving properties have been conjectured for the bilaplace Dirichlet problem in many versions. In this note we show that in any dimension there exist bounded smooth domains Ω such that even the solution of ∆u = 1 in Ω with the homogeneous Dirichlet boundary conditions u = uν = 0 on ∂Ω is sign-changing. In two dimensions this corresponds to the Kirchhoff-Love model of a clamped pla...

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response funct...

In this paper, we study the asymptotic behavior of solutions to Kirchhoff type stochastic plate equation driven by additive noise defined on unbounded domains. We first prove uniform estimates and then establish existence upper semicontinuity random attractors.

This paper proposes a pseudospectral approach for the Kirchhoff plate bending problem with uncertainties. The Karhunen-Loève expansion is used to transform the original problem to a stochastic fourth-order PDE depending only on a finite number of random variables. For the latter problem, its exact solution is approximated by a gPC expansion, with the coefficients obtained by the sparse grid met...