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DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗

NASA NTRS1988

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Sohn, Kiho D.↗

DOE OSTI2024

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Finite Element Analysis (FEA) for Water-Foam Fracturing of Granite Rock

In addition to the foam data that were obtained from literature and that were collected from the current study, simulation data was also generated from finite element analysis (FEA) conducted in this study using COMSOL Multiphysics software. The FEA models were built to simulate the experiments conducted at Oak Ridge National Laboratory (ORNL) on cement and granite samples. In these FEA models, temperature was kept at ambient while the pressure profile resembled the loading conditions during the ORNL experiments, where pressure was either monotonically increased or applied cyclically. The cement material was used as a model material and was used to study Von Mises stress and tensile stress distribution for different bore hole length geometry using a parametric sweep with water as fracturing fluid using solid-fluid interaction module. For the granite material, FEA models were developed for stress analysis of cylindrical samples with water or foam fluids. The solid mechanics module in COMSOL was implemented to solve for Von Mises stress and tensile stress. The fluid-structure interaction module was implemented to solve for water-foam interaction on granite cylinder with addition of fluid-loading on structure, i.e., large deformation in solid mechanics with no impact on fluid deformation. Foam was considered as a pseudo single-phase compressible fluid for which material properties were calculated from water and gas (nitrogen) phases. The density of foam is calculated as a function of the densities of water and nitrogen, while viscosity is a function of temperature. Four types of FEA analyses were modelled: 1. Monotonic injection with water 2. Monotonic injection with foam 3. Cyclic injection with water 4. Cyclic injection with foam All the COMSOL files are converted to a zip file which is save in .mph.

15 GEOTHERMAL ENERGY↗

DOE OSTI2020

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

In this paper, an extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.

multiscale↗

DOE OSTI2021

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1], [2], [3], [4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Here, the plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Finite element displacement analysis of a lung.

A method is given based on the technique of finite elements which determines theoretically the mechanical behavior of a lung-shaped body loaded by its own weight. The results of this theoretical analysis have been compared with actual measurements of alveolar size and pleural pressures in animal lungs.

Matthews, F. L.↗

NASA NTRS1976

On the explicit finite element formulation of the dynamic contact problem of hyperelastic membranes

Contact-impact problems involving finite deformation axisymmetric membranes are solved by the finite element method with explicit time integration. The formulation of the membrane element and the contact constraint conditions are discussed. The hyperelastic, compressible Blatz and Ko material is used to model the material properties of the membrane. Two example problems are presented.

Hallquist, J. O.↗

NASA NTRS1978

Finite element solution for beams using an element averaging technique

The article investigates the error in the computation of natural frequency through finite element models of the structures when elements of unequal length are chosen and then goes on to suggest an averaging technique for unequal length elements, with different structural properties. Using the element averaging technique, a typical structure has been analysed for its natural frequencies and the results are described.

Bhat, B. R.↗

NASA NTRS1978

Study on prestressed concrete reactor vessel structures. II-5: Crack analysis by three dimensional finite elements method of 1/20 multicavity type PCRV subjected to internal pressure

A three-dimensional finite elements analysis is reported of the nonlinear behavior of PCRV subjected to internal pressure by comparing calculated results with test results. As the first stage, an analysis considering the nonlinearity of cracking in concrete was attempted. As a result, it is found possible to make an analysis up to three times the design pressure (50 kg/sqcm), and calculated results agree well with test results.

Source record↗

NASA NTRS1979

Two-dimensional finite-element analyses of simulated rotor-fragment impacts against rings and beams compared with experiments

Finite element modeling alternatives as well as the utility and limitations of the two dimensional structural response computer code CIVM-JET 4B for predicting the transient, large deflection, elastic plastic, structural responses of two dimensional beam and/or ring structures which are subjected to rigid fragment impact were investigated. The applicability of the CIVM-JET 4B analysis and code for the prediction of steel containment ring response to impact by complex deformable fragments from a trihub burst of a T58 turbine rotor was studied. Dimensional analysis considerations were used in a parametric examination of data from engine rotor burst containment experiments and data from sphere beam impact experiments. The use of the CIVM-JET 4B computer code for making parametric structural response studies on both fragment-containment structure and fragment-deflector structure was illustrated. Modifications to the analysis/computation procedure were developed to alleviate restrictions.

Stagliano, T. R.↗

NASA NTRS1981

Exact finite elements for conduction and convection

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

Thornton, E. A.↗

NASA NTRS1981

Transonic flow computations in cascades using finite element method

Analysis of transonic flow through a cascade of airfoils is investigated using the finite element method. Development of a computational grid suitable for complex flow structures and different types of boundary conditions is presented. An efficient pseudo-time integration scheme is developed for the solution of equations. Modeling of the shock and the convergence characteristics of the developed scheme are discussed. Numerical results include a 45 deg staggered cascade of NACA 0012 airfoils with inlet flow Mach number of 0.8 and angles of attack 1, 0, and 1 deg.

Akay, H. U.↗

NASA NTRS1982

Novel solution of 2-D waveguides using the finite element method

A novel technique is described for solving 2-D waveguide equations using the finite element method. The full-wave equation is solved, thus automatically taking care of various inhomogeneities in the medium. The solution yields the transverse components of the field, which are useful for calculating far-field radiation patterns.

Katz, J.↗

NASA NTRS1981

Exact finite elements for conduction and convection

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Thornton, E. A.↗

NASA NTRS1983

A least squares finite element scheme for transonic flow around harmonically oscillating airfoils

The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.

Cox, C. L.↗

NASA NTRS1982

Computation of consistent boundary quantities in finite element thermal-fluid solutions

The consistent boundary quantity method for computing derived quantities from finite element nodal variable solutions is investigated. The method calculates consistent, continuous boundary surface quantities such as heat fluxes, flow velocities, and surface tractions from nodal variables such as temperatures, velocity potentials, and displacements. Consistent and lumped coefficient matrix solutions for such problems are compared. The consistent approach may produce more accurate boundary quantities, but spurious oscillations may be produced in the vicinity of discontinuities. The uncoupled computations of the lumped approach provide greater flexibility in dealing with discontinuities and provide increased computational efficiency. The consistent boundary quantity approach can be applied to solution boundaries other than those with Dirichlet boundary conditions, and provides more accurate results than the customary method of differentiation of interpolation polynomials.

Thornton, E. A.↗