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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

In this paper, we propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Lastly, various numerical experiments are used to demonstrate the robustness of the proposed solver.

58 GEOSCIENCES↗
NASA NTRS1999

System and Method for Finite Element Simulation of Helicopter Turbulence

The present invention provides a turbulence model that has been developed for blade-element helicopter simulation. This model uses an innovative temporal and geometrical distribution algorithm that preserves the statistical characteristics of the turbulence spectra over the rotor disc, while providing velocity components in real time to each of five blade-element stations along each of four blades. for a total of twenty blade-element stations. The simulator system includes a software implementation of flight dynamics that adheres to the guidelines for turbulence set forth in military specifications. One of the features of the present simulator system is that it applies simulated turbulence to the rotor blades of the helicopter, rather than to its center of gravity. The simulator system accurately models the rotor penetration into a gust field. It includes time correlation between the front and rear of the main rotor, as well as between the side forces felt at the center of gravity and at the tail rotor. It also includes features for added realism, such as patchy turbulence and vertical gusts in to which the rotor disc penetrates. These features are realized by a unique real time implementation of the turbulence filters. The new simulator system uses two arrays one on either side of the main rotor to record the turbulence field and to produce time-correlation from the front to the rear of the rotor disc. The use of Gaussian Interpolation between the two arrays maintains the statistical properties of the turbulence across the rotor disc. The present simulator system and method may be used in future and existing real-time helicopter simulations with minimal increase in computational workload.

McFarland, R. E.↗
DOE OSTI2018

Boundary coefficient determination for an eddy current problem based on the potential field method

We study a recovery problem for an unknown boundary coefficient relating to one material characteristic in an eddy current field. The field equations are represented in terms of the potential field method (T-ψ method) and can be solved numerically by the nodal finite element method. We introduce a measurement as an additional condition and prove the existence and uniqueness of the weak solution. Further, we present an iteration algorithm for the recovery problem and validate its efficiency by two numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

Abstract The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed $$u$$ u – $$p$$ p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Baek, Jonghyuk↗
DOE OSTI2022

Modeling Isothermal Reduction of Iron Ore Pellet Using Finite Element Analysis Method: Experiments & Validation

Iron ore pellet reduction experiments were performed with pure hydrogen (H2) and mixtures with carbon monoxide (CO) at different ratios. For direct reduction processes that switch dynamically between reformed natural gas and hydrogen as the reductant, it is important to understand the effects of the transition on the oxide reduction kinetics to optimize the residence time of iron ore pellets in a shaft reactor. Hence, the reduction rates were studied by varying experimental parameters such as the temperature (800, 850 & 900 °C), reactant gas flow rate (100, 150 & 200 cm3/min), pellet size and composition of the reactant gas mixture. The rate of reduction was observed to increase with an increase in temperature and reactant gas flow rate, but it decreased with an increase in pellet size. SEM greyscale analysis was performed to analyze the porosity and phase composition of partially reduced pellets. The porosity of the pellets was observed to increase from 0.3 for unreacted pellet to 0.42 for a completely reduced pellet. Energy-dispersive X-ray spectroscopy (EDAX) analysis was performed to identify the phases observed in the SEM images. The fraction of iron phase was observed to increase from the shell region of the pellet to the core region with an increase in the degree of reduction. A 2D-axisymmetric numerical model was developed on COMSOL Multiphysics, and it was validated using the conversion (X) vs. time curves obtained from each experiment. The model was able to accurately predict the total time needed for the complete conversion of a single iron ore pellet for multiple experiments. Effects of changes in the porosity and tortuosity of the pellet on the model were also studied and the rate of reduction was observed to be sensitive to changes in both porosity and tortuosity. The SEM analysis and the model results show that tortuosity is higher for pellets reduced with H2 than for pellets reduced with H2-CO gas mixtures.

08 HYDROGEN↗
NASA NTRS1976

On a 3-D singularity element for computation of combined mode stress intensities

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Atluri, S. N.↗
NASA NTRS1978

Critical study of higher order numerical methods for solving the boundary-layer equations

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

Wornom, S. F.↗
NASA NTRS1979

Mechanics of fracture - Fundamentals and some recent developments

An overview is presented of the fundamental aspects of and recent developments in fracture mechanics. Reference is made to linear elastic fracture mechanics including the state of stresses and displacements in the vicinity of cracks, effects of crack geometry and orientation on stress intensity factors, energy balance of Griffith, Irwin's stress intensity concept, and linear elastic fracture mechanics testing for fracture toughness. Other aspects of this paper include the non-linear behavior of materials and their influence on fracture mechanics parameters, consideration of viscoelasticity and plasticity, non-linear fracture toughness parameters as C.O.D., R-curve and J-integral, and a non-linear energy method, proposed by Liebowitz. Finite element methods applied to fracture mechanics problems are indicated. Also, consideration has been given to slow crack growth, dynamic effects on K(IC), Sih's criterion for fracture, Lee and Liebowitz's criterion relating crack growth with plastic energy, and applications of fracture mechanics to aircraft design. Suggestions are offered for future research efforts to be undertaken in fracture mechanics.

Liebowitz, H.↗
NASA NTRS1988

An adaptive remeshing method for finite element thermal analysis

A finite element remeshing approach that makes use of quadrilateral and triangular elements is described. The approach uses the solution on a previous mesh to create a new mesh. Meshes are completely unstructured with highly refined elements in regions of steep gradients and larger elements where gradients are smaller. Studies of convergence rates for heat conduction problems with exact solutions show that for problems with highly localized solution variations, the remeshing approach gives smaller solution errors with fewer unknowns than refinement of uniform, structured meshes.

Thornton, Earl A.↗
NASA NTRS1992

The free and forced vibrations of structures using the finite dynamic element method

In addition to an extensive review of the literature on exact and corrective displacement based methods of vibration analysis, a few theorems are proven concerning the various structural matrices involved in such analyses. In particular, the consistent mass matrix and the quasi-static mass matrix are shown to be equivalent, in the sense that the terms in their respective Taylor expansions are proportional to one another, and that they both lead to the same dynamic stiffness matrix when used with the appropriate stiffness matrix.

Fergusson, Neil J.↗
NASA NTRS1994

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗
NASA NTRS1996

Electromagnetic Scattering Analysis of Arbitrarily Shaped Material Cylinder by FEM-BEM Method

A hybrid method that combines the finite element method (FEM) and the boundary element method (BEM) is developed to analyze electromagnetic scattering from arbitrarily shaped material cylinders. By this method, the material cylinder is first enclosed by a fictitious boundary. Maxwell's equations are then solved by FEM inside and by BEM outside the boundary. Electromagnetic scattering from several arbitrarily shaped material cylinders is computed and compared with results obtained by other numerical techniques.

Deshpande, M. D.↗