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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

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

NAFEMS Finite Element Benchmarks for MDG Code Verification

Description: NAFEMS was originally founded at the United Kingdom's National Engineering Laboratory as the National Agency for Finite Element Methods and Standards. It was subsequently privatized as the not-for-profit organization NAFEMS, Ltd., but retains its mission ''To promote the safe and reliable use of finite element and related technology''. That mission has been pursued in part by sponsoring a series of studies that published benchmarked deemed suitable to assess the basic accuracy of engineering simulation tools. The early studies focused on FEA for linear solid and structural mechanics and then extended to nonlinear solid mechanics, eventually including contact. These benchmarks are complemented by educational materials concerning analysis technologies and approaches. More recently NAFEMS is expanding to consider thermal-fluid problems. Further information is available at www.nafems.org. Essentially all major commercial firms selling FEA for solid mechanics are members of NAFEMS and it seemed clear that Methods Development Group should leverage from this information resource, too. In 2002, W Program ASCI funding purchased a three-year membership in NAFEMS. In the summer of 2003 the first author hosted a summer graduate student to begin modeling some of the benchmark problems. We concentrated on NIKE3D, as the benchmarks are most typically problems most naturally run with implicit FEA. Also, this was viewed as a natural path to generate verification problems that could be subsequently incorporated into the Diablo code's test suite. This report documents and archives our initial efforts. The intent is that this will be a ''living document'' that can be expanded as further benchmarks are generated, run, interpreted and documented. To this end each benchmark, or related grouping, is localized in its own section with its own pagination. Authorship (test engineers) will be listed section by section.
Date: February 24, 2004
Creator: Greer, R & Ferencz, R M
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

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

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., Jr. & Johnson, Stanley J.
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

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

Physics-based Modeling of Brittle Fracture: Cohesive Formulations and the Application of Meshfree Methods

Description: Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically-based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of material, meaning that a finite material strength and work to fracture are included in the material description. In this study, we present both surface and bulk cohesive formulations for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well-suited to modeling fracture behavior. We describe the application of meshfree methods to both bulk and surface approaches to cohesive modeling. We present numerical examples highlighting the capabilities and shortcomings of the methods in order to identify which approaches are best-suited to modeling different types of fracture phenomena.
Date: December 1, 2000
Creator: Klein, P. A.; Foulk, J. W.; Chen, E. P.; Wimmer, S. A. & Gao, H.
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