Application of the meshless procedure for the elastoplastic torsion of prismatic rods

In this paper torsion of prismatic bars considering elastic-plastic material behavior is studied. Based on the Saint-Venant displacement assumption and the Romberg-Osgood model for the stress-strain relation, the boundary value problem for stress function is formulated. In reality an area of cross section of a bar has two regions: elastic with linear governing equation and plastic with non-linear governing equation. In the solution procedure, the meshless procedure based on the Homotopy Analysis Method HAM connected with the Method of Fundamental Solutions (MFS) and Radial Basis Functions (RBF) is applied. The considered nonlinear partial differential equation (PDE) is transform into a hierarchy of linear inhomogeneous PDEs. The accuracy of the obtained approximate solution is controlled by the number of components of the calculate solution, while the convergence of the process is monitored by an additional parameter of the method. The advantage of the proposed meshless approach is that it does not require the generation of a mesh on the domain or its boundary, but only using a cloud of arbitrary located nodes

Application of the method of fundamental solutions for inverse problems related to the determination of elasto-plastic properties of prizmatic bar

The problem of determining the elastoplastic properties of a prismatic bar from the given relation from experiment between torsional moment MT and angle of twist per unit of rod’s length θ is investigated as inverse problem. Proposed method of solution of inverse problem is based on solution of some sequences of direct problem with application of the Levenberg-Marquardt iteration method. In direct problem these properties are known and torsional moment as a function of angle of twist is calculated form solution of some non-linear boundary value problem. For solution of direct problem on each iteration step the method of fundamental solutions and method of particular solutions is used for prismatic cross section of rod. The non-linear torsion problem in plastic region is solved by means of the Picard iteration

Subextension of plurisubharmonic functions with weak singularities

We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity

Proposal for the creation of a national network of global studies high schools

This is a proposal to seek private and public funding to create a national network of global studies high schools (GSHS). The aim of a network of GSHSs is to enlarge the leadership corps of the next generation and to equip its members to address mounting global challenges to the security, material welfare, and freedoms of the American people, the citizens of open societies everywhere, and those who are striving to join their ranks.Title VI National Resource Center Grant (P015A060066)published or submitted for publicationnot peer reviewe

Aerothermal test results from the first flight of the Pegasus air-launched space booster

A survey of temperature measurements at speeds through Mach 8.0 on the first flight of the Pegasus air-launched booster system is discussed. In addition, heating rates were derived from the temperature data obtained on the fuselage in the vicinity of the wing shock interaction. Sensors were distributed on the wing surfaces, leading edge, and on the wing-body fairing or fillet. Side-by-side evaluations were obtained for a variety of sensor installations. Details of the trajectory reconstruction through first-stage separation are provided. Given here are indepth descriptions of the sensor installations, temperature measurements, and derived heating rates along with interpretations of the results

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

Viscomagnetoelastic Interactions in a Vortex Array in the Type–II Superconductor

The paper develops considerations on viscomagnetoelastic interactions in a vortex array in a type–II superconductor. It is well known that a magnetic field penetrates such a material along lines called vortices of a special structure. Each of them consists of a core of material in the normal state, i.e. a material in which Ohm’s law works and a surrounding where the supercurrent flows. The mean diameter of a core is called the coherence length. The penetration of the supercurrent outside the core exists in the London penetration depth. Since interactions among the vortices run with the help of the Lorenz force, the vortex field has elastic properties. Moreover, because of the normal state inside the vortex core also the viscosity of that field has been observed. The above situation occurs only between upper and lower magnetic field limits below the critical temperature regarding the phase diagram. The vortex field has a very interesting feature. In the vicinity of the lower magnetic field curve it possesses an ordered (quadratic or triangular) structure. Then going to the upper magnetic field limit that structure is losing its configuration behaving as a fluid. We assume smooth transition from ordered to disordered state althought it is much more complicated in nature. Following the above statements all the “material” coefficients characteristic for the vortex field are also dependent on the magnetic field and temperature. The main aim of the paper is a formulation of the stress – strain constitutive law consisting of the following features:• a coexistence of the ordered and disordered states,• the viscosity of the vortex field,• the dependence of the “material” coefficients related to the vortex field on the magnetic field.An application for YBCO ceramics that deals with the use of the proposed constitutive law in vortex field equations and results coming from that are presented. Numerical calculations concern wave propagation in depinned parallel vortex line field versus magnitude of the applied magnetic field