A two-dimensional finite element multigroup diffusion theory for neutral atom transport in plasmas

The power deposition and wall material erosion rates due to charge-exchange neutral atoms resulting from a recycling source at limiters in the TEXTOR and Tokamak Fusion Test Reactor tokamaks are reported. The analysis is carried out using a recently developed finite element, two-dimensional toroidal geometry diffusion theory, neutral atom transport theory, and the computer code FENAT. The power deposition and material erosion are highest at the limiter. The first wall suffers very little erosion except for the portion near the limiter.

A simple and novel finite element (FE) formulation is proposed to study the thermal post-buckling of composite and FGM columns with axially immovable ends and operating in severe thermal environment. A linear eigenvalue analysis gives the critical buckling temperature but practically the buckled columns can withstand additional thermal load beyond critical temperature, which can be obtained using von-Karman geometric nonlinearity, applicable for moderately large deflections. In the present study, the solution of the non-linear post-buckling problem is obtained by treating it as a linear eigenvalue problem using the concept of effective stiffness. Here, the total degrees of freedom (dof) of the discretized column are reduced and the post-buckling load is obtained without the need for iterative analysis. Comparison of the numerical results obtained from this FE formulation is in very good agreement with those obtained from the earlier FE formulations.

Laser-cooled gases offer an alternative to tip-based methods for generating high-brightness ion beams for focused ion beam applications. These sources produce ions by photoionization of ultracold neutral atoms, where the narrow velocity distribution associated with microkelvin-level temperatures results in a very low emittance, high-brightness ion beam. In a magneto-optical trap-based ion source, the brightness is ultimately limited by the transport of cold neutral atoms, which restricts the current that can be extracted from the ion-generating volume. We explore the dynamics of this transport in a 7Li magneto-optical trap ion source by performing time-dependent measurements of the depletion and refilling of the ionization volume in a pulsed source. An analytic microscopic model for the transport is developed, and this model shows excellent agreement with the measured results.

In this paper we describe our group efforts to develop a self-consistent, data-drivenmodel of the solar wind (SW) interaction with the local interstellar medium. The motion of plasma in this model is described with the MHD approach, while the transport of neutral atoms is addressed by either kinetic or multi-fluid equations. The model and its implementation in the Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS) are continuously tested and validated by comparing our results with other models and spacecraft measurements. In particular, it was successfully applied to explain an unusual SW behavior discovered by the Voyager 1 spacecraft, i.e., the development of a substantial negative radial velocity component, flow turning in the transverse direction, while the latitudinal velocity component goes to very small values. We explain recent SW velocity measurements at Voyager 1 in the context of our 3-D, MHD modeling. We also present a comparison of different turbulence models in their ability to reproduce the SW temperature profile from Voyager 2 measurements. The boundary conditions obtained at 50 solar radii from data-driven numerical simulations are used to model a CME event throughout the heliosphere.

In this paper, a finite element formulation is defined in the framework of the discontinuous Galerkin method. Discontinuous Galerkin (dG) methods are classically used in fluid mechanics, however recently their application in solid mechanics has become more vivid among scientists. Of special interest is their application in elliptic problems with constraints such as incompressibility which leads to volumetric locking phenomenon and also in some structural models of shells, plates and beams with compatibility constraints, which brings about shear locking [1]. While classical standard Galerkin methods must be continuous, dG methods can be applied for discontinuities across element boundaries, where a jump of a value (displacement) can be observed. In the present work, a dG method is applied to a linear elastic bar, where a weak discontinuity is allowed in the bar. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Finite element implementation of a non-local particle method for elasticity and fracture analysis

A computational study of operating regimes for poloidal divertors

A new continuum FE approach for fracture mechanics discontinuous problems

Nanoencapsulated phase change materials (nePCMs) – which are composed of a core with a phase change material and of a shell that envelopes the core – are currently under research for heat storage applications. Mechanically, one problem encountered in the synthesis of nePCMs is the failure of the shell due to thermal stresses during heating/cooling cycles. Thus, a compromise between shell and core volumes must be found to guarantee both mechanical reliability and heat storage capacity. At present, this compromise is commonly achieved by trial and error experiments or by using simple analytical solutions. On this ground, the current work presents a thermodynamically consistent and three-dimensional finite element (FE) formulation considering both solid and liquid phases to study thermal stresses in nePCMs. Despite the fact that there are several phase change FE formulations in the literature, the main novelty of the present work is its monolithic coupling – no staggered approaches are required – between thermal and mechanical fields. Then, the FE formulation is implemented in a computational code and it is validated against one-dimensional analytical solutions. Finally, the FE model is used to perform a thermal stress analysis for different nePCM geometries and materials to predict their mechanical failure by using Rankine’s criterion.

<p>The Dynamic Finite Element (DFE) theory is employed to calculate the natural frequencies and mode shapes of three-layered sandwich beams. Three formulations are developed and tested using a number of different numerical cases. The first two theories pertain to the analysis of straight beams while the third one is developed for the analysis of curved beams. The results from all three derivations agree well with published data that uses Classical Finite Element (FEM) theory and the Dynamic Stiffness Method (DSM) in the analysis of the free vibration behaviour of sandwich beams. For all test cases, the DFE results agree well with the published results as well as the FEM developed as an additional benchmark for the DFE. The results of the research are very encouraging and demonstrate that DFE is a valuable structural analysis tool that can be used in conjunction with FEM and DSM. </p>

A finite element formulation is developed including the fully coupled electrical-structural constitutive relations. An effort has been made to develop the most general formulation applicable to laminated composite plates with inclusion of piezoceramic sensors/actuators. To this end, the von Karman large deflection theory was included, due to the results obtained from the experiments conducted. Solution of the large deflection problem lead to an electrical-structural coupled tangent stiffness, which is believed to be the first time reported in the literature. paper presents comparison of the finite element simulation to experimental results for both static and dynamic piezoceramic sensors in addition to dynamic piezoceramic actuation. INTRODUCTION Piezoelectric material maintains a complex and intricate relationship between several physical sciences such as materials, thermal, electric fields, and elasticity. Evidence of the piezoelectric's complexity can be demonstrated by the seemingly continuous research conducted since its discovery in 1880 by Pierre and Jaques Curie. Much of the research set out to determine analytical models describing the piezoelectric phenomenon and lead to discrete devices such as extremely sharp crystal filters and stable oscillators. Mindlin developed classical methods describing the analysis on waves and vibrations in isotropic elastic plates concurrently with high frequency vibration of crystal plates. Allik and Hughes developed a solid, or three dimensional, finite element to model transducers and crystal oscillators. However, given that smart structures typically consist of thin piezoelectric layers attached to structures that are several orders of magnitude greater in thickness, the solid finite element formulation leads to an inherently inefficient process in which to model the complete physical structure. Subsequently Tzou and Tseng * Graduate Student, Student member AIAA. t Professor, Associate Fellow AIAA. This paper is declared a work of the U.S. Government and is not subject to copy right protection in the United States. formulated a new thin piezoelectric solid finite element in the form of shell and plate elements. When considering piezoelectrics in conjunction with structural members, linear piezoelectric theory simplifies the piezoelectric effect. Linear piezoelectric theory assumes an isothermal adiabatic process and quasi-static electric field equations. research presents a comparison of the fully coupled electricalstructural finite element analysis of an isotropic panel with a surface mounted piezoelectric patch to experimental results. PIEZOELECTRIC RELATIONS Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Linear piezoelectric theory yields an intrinsically coupled pair of piezoelectric constitutive equations. One describes the direct piezoelectric effect where the state of strain gives rise to an electric polarization, and the other describes the converse effect where an applied electrical field develops a state of strain. For a thin piezoelectric layer, the following constitutive relations result from linear piezoelectric theory (1)

The application of a finite shell element for composites containing piezo-electric polymers in vibration control

SUMMARYA novel finite element (FE) formulation with adaptive mesh rezoning for large deformation problems is proposed. The proposed method takes the advantage of the selective smoothed FE method (S‐FEM), which has been recently developed as a locking‐free FE formulation with strain smoothing technique. We adopt the selective face‐based smoothed/node‐based smoothed FEM (FS/NS‐FEM‐T4) and edge‐based smoothed/node‐based smoothed FEM (ES/NS‐FEM‐T3) basically but modify them partly so that our method can handle any kind of material constitutive models other than elastic models. We also present an adaptive mesh rezoning method specialized for our S‐FEM formulation with material constitutive models in total form. Because of the modification of the selective S‐FEMs and specialization of adaptive mesh rezoning, our method is locking‐free for severely large deformation problems even with the use of tetrahedral and triangular meshes. The formulation details for static implicit analysis and several examples of analysis of the proposed method are presented in this paper to demonstrate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd.

Neutral atom transport in the edge region of fusion plasmas is characterized by extreme geometrical complexity, mean-free-paths that vary from millimetres to metres over short distances, and many orders of magnitude variation in atom density. We have proposed and are developing an interface current integral transport method as a more practical alternative to the Monte Carlo method, which is currently used for such calculations. This particular formulation of interface current methodology is described, the accuracy of the several approximations that are made in implementing the methodology are evaluated by comparison with Monte Carlo, and correction factors and extensions of the methodology, which improve accuracy, are presented. The results are formulated so as to be generally applicable to any neutral particle transport application.

A 3D FDTD subgridding scheme based on a finite element (FE) formulation to solve Maxwell equations is presented. Derived from a variation formulation of two coupled problems with the use of Lagrange multipliers and mass lumping, an FDTD subgridding scheme is proposed and analyzed. The stability is discussed with the help of a discrete energy conservation. Some results demonstrate the efficiency and validity of the proposed method.