Circularly cylindrical layered media in plane elasticity

Layered Cylindrical Algebraic Decomposition

In this paper the idea of a Layered CAD is introduced, a truncation of a CAD to only high dimensional cells. Limiting to full-dimensional cells has already been investigated in the literature, but including another level can be beneficial for applications. A related topological property is defined and related to robotics motion planning. The distribution of cell dimensions in a CAD is investiga...

Topological Derivatives in Plane Elasticity

We present a method for construction of the topological derivatives in plane elasticity. It is assumed that a hole is created in the subdomain of the elastic body which is filled out with isotropic material. The asymptotic analysis of elliptic boundary value problems in singularly perturbed geometrical domains is used in order to derive the asymptotics of the shape functionals depending on the ...

Plane wave approximation in linear elasticity

In-Plane and out of Plane Free Vibration of U-Shaped AFM Probes Based on the Nonlocal Elasticity

Atomic force microscope (AFM) has been developed at first for topography imaging; in addition, it is used for characterization of mechanical properties. Most researches have been primarily focused on rectangular single-beam probes to make vibration models simple. Recently, the U-shaped AFM probe is employed to determine sample elastic properties and has been developed to heat samples locally. I...

Plane wave expansion of cylindrical functions

where V 2 is the two-dimensional Laplace operator and k is the wavenumber of the radiation field. The function Vstands for a typical component of the electric or magnetic field. In cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hn (kr ) exp (int~), where Hn is the Hankel function of integer order n while r and ot are a radial and an angular coordinate, re...