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Finite-Element Analysis of a Thick-Wall Tube Containing a Crater-Like Surface Flaw

Description: A three-dimensional finite-element elastic analysis is carried out for a thick-wall tube (as sued in typical LMFBR steam generators) that contains a surface flaw in the form of a paraboloid of revolution. Effects of the depth and aspect ratio of the flaw on the stress distribution and stress concentration in the tube are explored.
Date: June 1976
Creator: Majumdar, S.
Partner: UNT Libraries Government Documents Department

The Steepest Descent Method Using Finite Elements for Systems of Nonlinear Partial Differential Equations

Description: The purpose of this paper is to develop a general method for using Finite Elements in the Steepest Descent Method. The main application is to a partial differential equation for a Transonic Flow Problem. It is also applied to Burger's equation, Laplace's equation and the minimal surface equation. The entire method is tested by computer runs which give satisfactory results. The validity of certain of the procedures used are proved theoretically. The way that the writer handles finite elements is quite different from traditional finite element methods. The variational principle is not needed. The theory is based upon the calculation of a matrix representation of operators in the gradient of a certain functional. Systematic use is made of local interpolation functions.
Date: August 1981
Creator: Liaw, Mou-yung Morris
Partner: UNT Libraries

Visualization of higher order finite elements.

Description: Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
Date: April 1, 2004
Creator: Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H. & Khardekar, Rahul Vinay
Partner: UNT Libraries Government Documents Department

EMPHASIS/Nevada UTDEM user guide : version 1.0.

Description: The Unstructured Time-Domain ElectroMagnetics (UTDEM) portion of the EMPHASIS suite solves Maxwell's equations using finite-element techniques on unstructured meshes. This document provides user-specific information to facilitate the use of the code for applications of interest.
Date: March 1, 2005
Creator: Turner, C. David; Seidel, David Bruce & Pasik, Michael Francis
Partner: UNT Libraries Government Documents Department

Exact sub-grid interface correction schemes for elliptic interface problems

Description: We introduce a non-conforming finite element method for second order elliptic interface problems. Our approach applies to problems in which discontinuous coefficients and singular sources on the interface may give rise to jump discontinuities in either the solution or its normal derivative. Given a standard background mesh and an interface that passes between elements, the key idea is to construct a singular correction function which satisfies the prescribed jump conditions, providing accurate sub-grid resolution of the discontinuities. Utilizing the closest point extension and an implicit interface representation by the signed distance function, an algorithm is established to construct the correction function. The result is a function which is supported only on the interface elements, represented by the regular basis functions, and bounded independently of the interface location with respect to the background mesh. In the particular case of a constant second order coefficient, our regularization by singular function is straightforward, and the resulting left-hand-side is identical to that of a regular problem without introducing any instability. The influence of the regularization appears solely on the right-hand-side, which simplifies the implementation. In the more general case of discontinuous second order coefficients, a normalization is invoked which introduces a constraint equation on the interface. This results in a problem statement similar to that of a saddle-point problem. We employ two-level-iteration as the solution strategy, which exhibits aspects similar to those of iterative preconditioning strategies.
Date: December 9, 2008
Creator: Huh, J.S. & Sethian, J.A.
Partner: UNT Libraries Government Documents Department

A balancing domain decomposition method by constraints for advection-diffusion problems

Description: The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.
Date: December 10, 2008
Creator: Tu, Xuemin & Li, Jing
Partner: UNT Libraries Government Documents Department

The Influence of Construction Step Sequence and Nonlinear Material Behavior on Cracking of Earth and Rock-Fill Dams: Preliminary Study

Description: Summary: This report is a review of the materials, specifications, procedures, equipment, and testing pertinent to construction and compaction control of the earth-fill embankment of Littleville Dam, Westfield River, Mass., constructed by the U. S. Army Engineer Division, New England.
Date: December 1970
Creator: Strohm, William E. & Johnson, Stanley J.
Partner: UNT Libraries Government Documents Department

Modeling aspects of the dynamic response of heterogeneous materials

Description: In numerical simulations of engineering applications involving heterogeneous materials capturing the local response coming from a distribution of heterogeneities can lead to a very large model thus making simulations difficult. The use of homogenization techniques can reduce the size of the problem but will miss the local effects. Homogenization can also be difficult if the constituents obey different types of constitutive laws. Additional complications arise if inelastic deformation. In such cases a two-scale approach is prefened and tills work addresses these issues in the context of a two-scale Finite Element Method (FEM). Examples of using two-scale FEM approaches are presented.
Date: January 1, 2009
Creator: Ionita, Axinte; Clements, Brad & Mas, Eric
Partner: UNT Libraries Government Documents Department

Calculation of positron observables using a finite-element-based approach

Description: We report the development of a new method for calculating positron observables using a finite-element approach for the solution of the Schrodinger equation. This method combines the advantages of both basis-set and real-space-grid approaches. The strict locality in real space of the finite element basis functions results in a method that is well suited for calculating large systems of a thousand or more atoms, as required for calculations of extended defects such as dislocations. In addition, the method is variational in nature and its convergence can be controlled systematically. The calculation of positron observables is straightforward due to the real-space nature of this method. We illustrate the power of this method with positron lifetime calculations on defects and defect-free materials, using overlapping atomic charge densities.
Date: November 4, 1998
Creator: Klein, B. M.; Pask, J. E. & Sterne, P.
Partner: UNT Libraries Government Documents Department

Parallelization of an unstructured grid, hydrodynamic-diffusion code

Description: We describe the parallelization of a three dimensional, un structured grid, finite element code which solves hyperbolic conservation laws for mass, momentum, and energy, and diffusion equations modeling heat conduction and radiation transport. Explicit temporal differencing advances the cell-based gasdynamic equations. Diffusion equations use fully implicit differencing of nodal variables which leads to large, sparse, symmetric, and positive definite matrices. Because of the unstructured grid, the off-diagonal non-zero elements appear in unpredictable locations. The linear systems are solved using parallelized conjugate gradients. The code is parailelized by domain decomposition of physical space into disjoint subdomains (SDS). Each processor receives its own SD plus a border of ghost cells. Results are presented on a problem coupling hydrodynamics to non-linear heat cond
Date: May 20, 1998
Creator: Milovich, J L & Shestakov, A
Partner: UNT Libraries Government Documents Department

Nonlinear Dynamics of a Stack/Cable System

Description: In this study, we developed a coupled model of wind-induced vibration of a stack, based on an unsteady-flow theory and nonlinear dynamics of the stack's heavy elastic suspended cables. Numerical analysis was performed to identify excitation mechanisms. The stack was found to be excited by vortex shedding. Once lock-in resonance occurred, the cables were excited by the transverse motion of the stack. Large-amplitude oscillations of the cables were due to parametric resonance. Appropriate techniques have been proposed to alleviate the vibration problem.
Date: July 1995
Creator: Cai, Y. & Chen, Shoei-Sheng
Partner: UNT Libraries Government Documents Department

Accuracy of the Finite Analytic Method for Scalar Transport Calculations

Description: The accuracy of the finite analytic method of discretizing fluid flow equations is assessed through calculations of multidimensional scalar transport. The transport of a scalar function in a uniform velocity flow field inclined with the finite-difference grid lines is calculated for a range of grid Peclet numbers and flow skewness. The finite analytic method is observed to be superior to the approach of constructing finite-difference analogs from locally one-dimensional resolution of the flow vector. However, the finite analytic method also produces appreciable errors locally in regions of steep variations, under conditions of large grid Peclet numbers, and skewness of the streamlines.
Date: September 1984
Creator: Vanka, S. P.
Partner: UNT Libraries Government Documents Department

A Combined Experimental and Computational Approach for the Design of Mold Topography that Leads to Desired Ingot Surface and Microstructure in Aluminum Casting.

Description: A stabilized equal-order velocity-pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume-averaging method. The analysis is performed in a single domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline-upwind/Petrov-Galerkin), PSPG (pressure stabilizing/Petrov-Galerkin) and DSPG (Darcy stabilizing/Petrov-Galerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG-based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary-alloy.
Date: May 27, 2004
Creator: Dr. Zabaras, N. & Samanta, D.
Partner: UNT Libraries Government Documents Department

ALEGRA : version 4.6.

Description: ALEGRA is an arbitrary Lagrangian-Eulerian multi-material finite element code used for modeling solid dynamics problems involving large distortion and shock propagation. This document describes the basic user input language and instructions for using the software.
Date: January 1, 2005
Creator: Wong, Michael K. W.; Summers, Randall M.; Petney, Sharon Joy Victor; Luchini, Christopher Bernard; Drake, Richard Roy; Carroll, Susan K. et al.
Partner: UNT Libraries Government Documents Department

ALEGRA-MHD : version 4.6

Description: ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling resistive magnetohydrodynamic, thermal conduction, and radiation emission effects.
Date: January 1, 2005
Creator: Garasi, Christopher Joseph; Cochrane, Kyle Robert; Mehlhorn, Thomas Alan; Haill, Thomas A.; Summers, Randall M. & Robinson, Allen Conrad
Partner: UNT Libraries Government Documents Department

Visualizing higher order finite elements :final report.

Description: This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Date: November 1, 2005
Creator: Thompson, David C. & PÔebay, Philippe Pierre
Partner: UNT Libraries Government Documents Department

High fidelity frictional models for MEMS.

Description: The primary goals of the present study are to: (1) determine how and why MEMS-scale friction differs from friction on the macro-scale, and (2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction. Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of 'pre-sliding tangential deflections' (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load. Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity. Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include ...
Date: October 1, 2004
Creator: Carpick, Robert W.; Reedy, Earl David, Jr.; Bitsie, Fernando; de Boer, Maarten Pieter; Corwin, Alex David; Ashurst, William Robert et al.
Partner: UNT Libraries Government Documents Department

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.

Description: In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of the Navier-Stokes system first presented in [25]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.
Date: April 1, 2007
Creator: Shadid, John Nicolas (Sandia National Laboratories, Albuquerque, NM); Elman, Howard (University of Maryland, College Park, MD); Shuttleworth, Robert R. (University of Maryland, College Park, MD); Howle, Victoria E. & Tuminaro, Raymond Stephen
Partner: UNT Libraries Government Documents Department

Simulating Photons and Plasmons in a Three-dimensional Lattice

Description: Three-dimensional metallic photonic structures are studied using a newly developed mixed finite element-finite difference (FE-FD) code, Curly3d. The code solves the vector Helmholtz equation as an eigenvalue problem in the unit cell of a triply periodic lattice composed of conductors and/or dielectrics. The mixed FE-FD discretization scheme ensures rapid numerical convergence of the eigenvalue and allows the code to run at low resolution. Plasmon and photonic band structure calculations are presented.
Date: September 3, 2002
Creator: Pletzer, A. & Shvets, G.
Partner: UNT Libraries Government Documents Department