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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Full-wave modeling of RF waves in fusion plasmas with finite element method: Progress in past decades and its future role

This paper reviews the progress in computing radio frequency (RF) wave fields in fusion plasmas, specifically focusing on simulations utilizing the finite element method (FEM) over the past few decades. Computing RF wave fields in fusion plasmas presents unique challenges due to large simulation domains, complex antenna structures, non-local dielectric properties, and wide ranges of spatial scales. It highlights key developments and outlines future directions, primarily addressing waves in the ion cyclotron (IC) to lower hybrid (LH) frequency range. We begin with briefly revisiting earlier developments before the widespread availability of modern computer-aided engineering (CAE) software based on FEM. This historical perspective illuminates early progress and the physics difficulties that motivated ongoing work within the community. Modern wave simulations for RF antennas based on FEM are characterized by the use of detailed 3D antenna model geometry generated from engineering CAD software and localized wave dielectric model. Significant advancements have also been made in improving physics models to include phenomena such as RF sheath rectification and wave scattering. FEM-based RF simulations have also been applied to compute wave propagation in the core region, where the inclusion of non-local dielectric response is crucial. This is a challenging goal, and several promising approaches have been proposed in this area. Additionally, RF simulation development initiatives based on open-source libraries have gained popularity, demonstrating scalability and flexibility in extending physics models. This paper will discuss the advantages and disadvantages of using such a publicly available FEM library.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1987

Multiple-mode nonlinear free and forced vibrations of beams using finite element method

Effects of large deflection geometric nonlinearity and multiple modes for free and forced vibrations of beams are investigated. Inplane displacement and inplane inertia are included in the formulation. The finite element method is employed. A harmonic force matrix is derived for forced vibration analysis. The relations of amplitude, frequency ratio and forcing intensity for beams of different boundary conditions and various load conditions are presented.

Mei, Chuh↗
NASA NTRS1982

Reliability of the finite element method for calculating free edge stresses in composite laminates

The interlaminar normal stress distributions along the interface between the +45 deg and -45 deg plies of a graphite/epoxy laminate, obtained by various investigators, were found to disagree in both magnitude and sign. The reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated. The history of the edge-stress problem is reviewed, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed. The finite element analysis in these problems yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a + or -45 deg ply laminate near the singularity were similar to those of the two elasticity problems, demonstrating the methods, accuracy for calculating interlaminar stresses in composite laminates. The disagreement between the numerical methods was attributed to the unsymmetric stress tensor at singularity.

Whitcomb, J. D.↗
NASA NTRS1980

Application of a Galerkin finite element method to atmospheric transport problems

Numerical simulation of the movement of a contaminant within the atmosphere presents difficulties due to the multidimensionality of the problem and the fact that the horizontal transport is usually convection dominated, that the boundary conditions are mixed, and that both slow and fast atmospheric chemical reactions can be important. In this study, numerical experiments using a Crank-Nicolson Galerkin finite element method to solve the time-dependent partial differential equations demonstrate the applicability and accuracy of this method for the variety of conditions encountered in atmospheric pollutant modeling. The Crank-Nicolson Galerkin method using piecewise linear, piecewise cubic Hermite polynomials, and upwind finite elements is shown to accurately model the pure convection of initial wave forms. Numerical results studying the interactions of convection, diffusion, chemical reaction, pollutant removal, and the effects of contaminant emission source strength, source location and multiple sources are also presented.

Carmichael, G. R.↗
NASA NTRS1985

Finite element method for nonlinear forced vibrations of circular plates

Geometric nonlinearities for large amplitude free and forced vibrations of circular plates are investigated. Inplane displacement and inertia are included in the formulation. Finite element method is used. Harmonic force matrix for nonlinear forced vibration analysis is introduced and derived. Various out-of-plane and inplane boundary conditions are considered. The relations of amplitude - frequency ratio for different boundary conditions and various loads conditions are presented.

Decha-Umphai, K.↗
DOE OSTI2024

Creep and Creep Fracture Modeling with Surrogate Creep Models and the Extended Finite Element Method

Alloy components in advanced nuclear reactors will be subjected to environmental conditions that could include high temperatures, irradiation, and exposure to corrosive salts. These conditions could lead to the formation of crack-like defects, which could grow over time in a mechanism known as creep crack growth (CCG). Predicting growth rates of these defects is important for assessing the safe operating life of advanced reactors. This project documents progress toward developing and testing next-generation data-driven constitutive models for deformation creep. It also documents the application of the extended finite element method in conjunction with surrogate creep models to predict CCG parameters under a variety of conditions. These important incremental developments contribute to the longer-term objective of developing microstructure-aware constitutive models that can be used for predicting creep deformation and CCG at the component scale with improved accuracy.

36 MATERIALS SCIENCE↗
NASA NTRS1987

Exact finite element method analysis of viscoelastic tapered structures to transient loads

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Spyrakos, Constantine Chris↗
NASA NTRS2011

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Gherlone, Marco↗
NASA NTRS1989

Comparison of boundary element and finite element methods in spur gear root stress analysis

The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.

Sun, H.↗
NASA NTRS1987

Adaptive finite element methods for high-speed compressible flows

An adaptive finite element algorithm for solving the unsteady Euler equations is described. The finite element algorithm is based on a Taylor/Galerkin formulation and uses a very fast and efficient data structure to refine and unrefine the grid in order to optimize the approximation. A general version of the method which can be applied to moving grids with sliding interfaces is given, and results for a transient supersonic calculation of rotor-stator interaction are presented.

Oden, J. T.↗
NASA NTRS1979

A shock capturing application of the finite element method

The paper is concerned with the development of finite element algorithms for the solution of viscous compressible flow problems with possible embedded shocks and recirculation regions. As a first step, the calculation in Cartesian coordinates of uniform flow on a rectangular region which encounters an embedded oblique shock with known turning angle is considered. A code is developed which is then used for computation of the boattail plume simulator problem in cylindrical coordinates. Oblique shock calculations are performed and the results are compared with a known finite difference solution.

Cooke, C. H.↗
NASA NTRS1988

A global-local finite element method suitable for parallel computations

A global-local finite element analysis procedure is developed based on the fast convergent nature of FEM in displacement. A special scheme is used to utilize the global displacement solution as boundary conditions for local regions of interest. In the local region, a refined mesh is used for further stress analysis. This global-local procedure can be easily programmed in parallel on MIMD multi-processor computers for significant time savings. A Sequent Balance 21000 system is used for demonstrating the parallel programming.

Sun, C. T.↗
DOE OSTI2025

A note on the reliability of goal-oriented error estimates for Galerkin finite element methods with nonlinear functionals

Here, we consider estimating the discretization error in a nonlinear functional J (u) in the setting of an abstract variational problem: find u ϵ $\mathscr{V}$ such that B (u, φ) = L (φ) ∀φ ϵ $\mathscr{V}$, as approximated by a Galerkin finite element method. Here, $\mathscr{V}$ is a Hilbert space, B (. , .) is a bilinear form, and L (∙) is a linear functional. We consider well-known error estimates η of the form J (u) - J (u h ) ≈ η = L (z) - B (u h , z), where u h denotes a finite element approximation to u, and z denotes the solution to an auxiliary adjoint variational problem. We show that there exist nonlinear functionals for which error estimates of this form are not reliable, even in the presence of an exact adjoint solution z. An estimate η is said to be reliable if there exists a constant C ϵ $\mathbb{R}$ >0 independent of u h such that |J (u) - J (u h )| ≤ C|η|. We present several example pairs of bilinear forms and nonlinear functionals where reliability of η is not achieved.

A posteriori↗
NASA NTRSDate not supplied

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method (FEM) models. Geometry measurement methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps of how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the preprocessing methods and results from Py_TIGIRS are provided and compared for Composite Test Articles (CTA) 8.2, 8.2B, and 8.3. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future developments of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Geometric imperfections↗
NASA NTRSDate not supplied

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method (FEM) models. Geometry measurement methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps of how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the preprocessing methods and results from Py_TIGIRS are provided and compared for Composite Test Articles (CTA) 8.2, 8.2B, and 8.3. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future developments of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Geometric imperfections↗
NASA NTRSDate not supplied

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric surface imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method models. Data collection methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps on how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the pre-processing methods and results from Py_TIGIRS are provided and compared for Composite Test Article (CTA) 8.2B. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future development of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Sandwich structures↗
NASA NTRS2004

Discontinuous Galerkin Finite Element Method for Parabolic Problems

In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.

Kaneko, Hideaki↗