In this work we derive by $\Gamma$ -convergence techniques a model for brittle fracture linearly elastic plates. Precisely, start from thin film with positive thickness $\rho$ and study the limit as tends to $0$ . The analysis is performed no priori restrictions on admissible displacements geometry of set. characterized Kirchhoff-Love type structure.

We study delamination in a sandwich panel due to transient finite plane strain elastic deformations caused by local water slamming loads and use the boundary element method to analyze motion of water and the finite element method to determine deformations of the panel. The cohesive zone model is used to study delamination initiation and propagation. The fluid is assumed to be incompressible and...

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal...

In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff index. During the past decade these parameters have been applied in organic chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules that have ...

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...