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Results for “hierarchical finite element”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A hierarchical finite element approach for integrated thermal-structural analysis

A hierarchical finite element approach for thermal-structural analysis is presented. The approach employs a common nodal discritization and seeks improvements in the accuracy of the analyses by using hierarchical interpolation functions with nodeless variables. The effectiveness of the integrated approach is assessed for three applications with two-dimensional elements by comparison with conventional finite element thermal-structural solutions. Improvements in the accuracy of temperatures and thermal-stresses are demonstrated. The applications demonstrate the practical importance of having flexibility in refining each analysis independently while maintaining a common discretization, and show that the hierarchical approach offers potential for the development of a general method for integrated thermal-structural analysis.

Thornton, E. A.↗
DOE OSTI2022

Finite Element Modeling of Diffusion in Fractured Porous Media by Using Hierarchical Material Properties

Abstract Fractured porous media challenge modeling approaches due to high computational costs and excessive mesh refinement imposed by the extreme scale variability of fractures and the heterogeneity of the surrounding porous rock. To overcome such difficulties, we utilize the hierarchical finite element method ( Hi ‐FEM) that has been developed previously to simulate the electrical potential distribution in complex geologic environments. The method employs the hierarchical basis functions in classical finite element analysis to enable representation of material properties on each dimensional component of a given 3D unstructured finite element, thereby inherently allowing for interactions at the boundary between fracture and a host rock. In this study, we extend its application to transient fluid flow and heat conduction in the Laplace domain. Time‐domain flow solutions are obtained by numerical inverse Laplace transform. We evaluate the accuracy of the method using different flow models and demonstrate its robustness for large‐scale, rock mass models featuring complex fracture networks. Moreover, for the computation of nodal Darcian velocity fields in fractured porous media where the fractures are represented as 2D features, a new approach that employs the Yeh's Galerkin model for both volume and facet elements is proposed. Results show that Hi ‐FEM can produce accurate flow solutions for fractured porous media without any need of coupling or transfer mechanism while still being computationally economical and numerically robust, even for large‐scale simulations.

Beskardes, G. D.↗
NASA NTRS1988

Adaptive p-version based finite element formulations for thermal modeling/analysis of structural configurations

Adaptive p-version based hierarchical finite element formulations in conjunction with a posteriori error estimation concepts are described with emphasis on applicability for thermal modeling/analysis of structural configurations. The basic concepts and formulations of hierarchical p-versiion finite element for thermal analysis are first described. A posteriori error estimation features are utililzed to steer the process of adaptive refinement. Several configurations comprised of one-dimensional structures are evaluated to validate the applicability of the proposed formulations and to demonstrate the potential of the p-version adaptive formulations for thermal modeling/analysis. The methodology offers potential and promises to be an attractive alternative to conventional finite element thermal modeling/analysis approaches.

Tamma, Kumar K.↗
NASA NTRS1992

Hierarchical flux-based thermal-structural finite element analysis method

A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.

Polesky, Sandra P.↗
DOE OSTI2021

inp2cjw

inp2cjw is a utility program for hierarchical finite element analysis which converts Abaqus formatted (inp) model output from CUBIT to a format (cjw) for HFEM and HFEM-Hydro modeling codes while introducing volume, facet, and edge material properties into the model. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-4551 O

Weiss, ChesterJ↗
NASA NTRS1996

A Parallel Multilevel Spectral Element Scheme

A parallel multilevel strategy is developed using spectral (p) finite elements. Hierarchic bases are particularly well suited since the element matrices and vectors are nested and the multilevel projections easiliy performed. Since the basis degree is used to specify the multigrid level, an EBE strategy is natural br the multilevel technique. Results are presented for two candidate nonlinear elliptic transport problems: the augmented drift-diffusion equations of semiconductor device modeling and the stream function-vorticity equations of incompressible fluid dynamics.

Davis, M. B.↗
DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗
NASA NTRS1984

On the development of hierarchical solution strategies for nonlinear finite element formulations

This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.

Padovan, J.↗
NASA NTRS1985

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗
NASA NTRS1982

Implementation of a C-1 triangular element based on the P-version of the finite element method

The implementation of a computer code CONE (for C(1) continuity) based on the p-version of the finite element method is described. A hierarchic family of triangular finite elements of degree p 5 is used. This family enforces C(1)-continuity across interelement boundaries, and the code is applicable to fourth order partial differential equations in two independent variables, in particular to the biharmonic equation. Applications to several benchmark problems in plate bending are presented. Sample results are examined and compared with theoretical predictions. In particular the analysis of the bending of a rhombic plate shows a significant improvement over othr published results.

Wang, D. W.↗
NASA NTRS2002

Finite Element A Posteriori Error Estimation for Heat Conduction

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Lang, Christapher G.↗
NASA NTRS1993

MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements

MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.

Mitchell, William F.↗
DOE OSTI2021

Hierarchical model reduction driven by a proper orthogonal decomposition for parametrized advection-diffusion-reaction problems

This work combines the Hierarchical Model (HiMod) reduction technique with a standard Proper Orthogonal Decomposition (POD) to solve parametrized partial differential equations for the modeling of advection-diffusion-reaction phenomena in elongated domains (e.g., pipes). This combination leads to what we define as HiPOD model reduction, which merges the reliability of HiMod reduction with the computational efficiency of POD. Two HiPOD techniques are presented and assessed by an extensive numerical verification.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The effects of well damage and completion designs on geoelectrical responses in mature wellbore environments

Well integrity is one of the major concerns in long-term geologic storage sites due to the potential risk of well leakage and groundwater contamination. Evaluating changes in electrical responses due to energized steel-cased wells has the potential to quantify and predict possible wellbore failures because any kind of breakage or corrosion along highly conductive well casings will have an impact on the distribution of the subsurface electrical potential. However, realistic wellbore-geoelectrical models that can fully capture fine-scale details of well completion design and the state of well damage at the field scale require extensive computational effort, or they can even be intractable to simulate. To overcome this computational burden while still keeping the model realistic, we have used the hierarchical finite-element method that represents electrical conductivity at each dimensional component (1D edges, 2D planes, and 3D cells) of a tetrahedral mesh. This allows well completion designs with real-life geometric scales and well systems with realistic, detailed, progressive corrosion and damage in our models. We have developed a comparison of possible discretization approaches of a multicasing completion design in the finite-element model. The effects of the surface casing and the coupling between concentric well casings as well as the effects of the degree and the location of well damage on the electrical responses are also examined. As a result, we analyze real surface electric field data to detect wellbore integrity failure associated with damage.

58 GEOSCIENCES↗
NASA NTRS2017

Comparison of Multiscale Method of Cells-Based Models for Predicting Elastic Properties of Filament Wound C/C-SiC

Three different multiscale models, based on the method of cells (generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the following multiscale modeling strategies were employed: Concurrent multiscale modeling of all phases using the generalized method of cells, synergistic (two-way coupling in space) multiscale modeling with the generalized method of cells, and hierarchical (one-way coupling in space) multiscale modeling with the high fidelity generalized method of cells. The three models are validated against data from a hierarchical multiscale finite element model in the literature for a repeating unit cell of C/C-SiC. Furthermore, the multiscale models are used in conjunction with classical lamination theory to predict the stiffness of C/C-SiC plates manufactured via a wet filament winding and liquid silicon infiltration process recently developed by the German Aerospace Institute.

multiscale modeling↗
NASA NTRS1989

Hierarchic plate and shell models based on p-extension

Formulation of hierarchic sequences of finite element models for beams, arches, plates and shells based on the principle of virtual work is described. The exact solutions corresponding to models in the hierarchic sequence converge to the exact solution of the fully three-dimensional problem of linear elasticity. The stopping criterion is that the functionals of interest must be substantially independent of the choice of the model. This process is closely related to p-extensions. Aspects of implementation are discussed in connection with axisymmetric shells and an example is presented. An application of superconvergent extraction methods for the computation of stress resultants is demonstrated.

Szabo, B. A.↗