In this paper, we derive a sharp observability inequality for Kirchhoff plate equations with lower order terms in an unbounded domain Ω of lR. More precisely, when the observation is assumed to be located in a subdomain ω such that Ω \ ω is bounded and the observation time T > 0 is sufficiently large, we establish an observability estimate with an explicit observability constant for Kirchhoff p...

In this paper we investigate the interaction of fluid flow with a thin porous elastic layer. We consider two fluid-filled bulk domains which are separated by periodically perforated layer consisting and an solid part. Thickness periodicity order ϵ, where ϵ is small compared to size domains. The described instationary Stokes equation via linear elasticity. main contribution rigorous homogenizati...

Abstract This is the first part of a two-part article on hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We present derivation new model, focus mechanics deformation. Accounting for stress distribution in direction affects accuracy calculating deformed-configuration position, and consequently nonlinear response shell. The improvement beyond what we get from acc...

Structures that are 3D printed by an extrusion process have periodic geometrical heterogeneity whose influence on the final stiffness properties is not extensively discussed in existing literature. The objective of this article to quantify effect local lace geometry anisotropy extrusion-based 3d structures. A numerical homogenisation scheme implemented compute equivalent homogeneous Kirchhoff–L...

We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The beams are discretised by the CutFEM technique of letting the basis functions of the plate represent also the beams which are allowed to pass through the...

Abstract The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. interaction between layers is taken into account due to van der Waals forces. investigation based on nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. effect Lorentz force Maxwell’s equations. go...

We develop a finite-element method for the simulation of dynamic shell fracture and fragmentation based on cohesive models of fracture. We assume the shells to be thin and to obey the Kirchhoff-Love theory. The shell is spatially discretized by means of subdivision shell elements. Fracture is allowed only along element edges and is assumed to be governed by a cohesive law. When coupled to the s...

A thin shell finite element approach based on Loop’s subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a...