We present two new recovery-based a posteriori error estimates for the Hellan–Herrmann–Johnson method in Kirchhoff–Love plate theory. The first estimator uses postprocessed deflection and controls \(L^2\) moment discrete \(H^2\) error. second one \(L^2\times H^1\) total utilizes superconvergent field deflection. effectiveness of theoretical results is numerically validated several experiments.

I present a method for anti-aliasing Kirchhoff imaging operators that improves the resolution of the image by properly imaging aliased components of the recorded data that would be suppressed by standard anti-aliasing methods for Kirchhoff operators. The proposed method succeeds in imaging “beyond aliasing” without generating aliasing noise because it exploits a priori knowledge on the dipspect...

Elastic theory of low-dimensional continua and its applications in bio-and nano-structures This review presents the elastic theory of low-dimensional (one-and two-dimensional) continua and its applications in bio-and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional continua , is briefly described through Cartan moving frame method. The...

In this paper‎, ‎we consider the following Kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$uin H^{1}(mathbb{R}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive ...

The Kirchhoff-Love plate model is a widely used in the analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions can be viewed as certain limits of displacements and stresses for elastic plates where the thickness tends to zero. In this paper, we consider the problem from a different point of view and derive computable upper bounds of the difference between the exact three...

In this paper, we explore whether the Fresnel term can be used to improve the predictions of the Beckmann–Kirchhoff (B-K) model for moderately rough surfaces. Our aim in developing this model is to describe subsurface scattering effects for surfaces of intermediate roughness. We use the BRDF measurements from the CUReT database to compare the predictions of the Fresnel correction process with a...

In this article, we study a Kirchhoff type problem with a positive parameter λ,

In this article, we apply the Nehari manifold method to study the Kirchhoff type equation

A layer-wise third order shear and normal deformable plate/shell theory (TSNDT) incorporating a cohesive zone model (CZM) is used to study the initiation and growth of delamination in straight and curved laminated beams. Upon satisfaction of the delamination criteria at a point on the interface between two layers, displacements there of two abutting points on the interface between the two layer...