In this paper we illustrate the use of the Beckmann-Kirchhoff model for analysing rough surface reflectance. The Beckmann-Kirchhoff model is a physical model that describes the reflectance of light from rough surfaces. The parameter of the model is the surface slope, or ratio of the surface roughness to the correlation length. We show how this parameter may be estimated using pairs of surface i...

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelasti...

For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for inverse determining smooth cavities inside a thin isotropic cylinder from single boundary measurement traction and displacement. The result is obtained by reformulating GPS as Kirchhoff–Love plate-like terms Airy function, using strong unique continuation at plate...

Abstract In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The Hessian is derived based on second-order Taylor series expansion. NOM does not require any shape functions and associated derivatives as ’classical’ approaches such FEM, drastically facilitating implementation. Furthermore, higher order continuous, which exploited thin pl...

For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

Abstract In the present work, two-phase integral theory of elasticity developed in Barretta et al. (Phys E 97:13–30, 2018) for nano-beams is generalized to model two-dimensional nano-continua. Notably, a well-posed mixture local/stress-driven nonlocal proposed accurately predict size effects Kirchhoff axisymmetric nanoplates. The key idea express elastic radial curvature as convex combination l...