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NASA NTRS1985

Shape design sensitivity analysis using domain information

A numerical method for obtaining accurate shape design sensitivity information for built-up structures is developed and demonstrated through analysis of examples. The basic character of the finite element method, which gives more accurate domain information than boundary information, is utilized for shape design sensitivity improvement. A domain approach for shape design sensitivity analysis of built-up structures is derived using the material derivative idea of structural mechanics and the adjoint variable method of design sensitivity analysis. Velocity elements and B-spline curves are introduced to alleviate difficulties in generating domain velocity fields. The regularity requirements of the design velocity field are studied.

Seong, Hwal-Gyeong↗

NASA NTRS1996

Radiation Characteristics of Cavity Backed Aperture Antennas in Finite Ground Plane Using the Hybrid FEM/MoM Technique and Geometrical Theory of Diffraction

A technique using hybrid Finite Element Method (FEM)/Method of Moments (MoM), and Geometrical Theory of Diffraction (GTD) is presented to analyze the radiation characteristics of cavity fed aperture antennas in a finite ground plane. The cavity which excites the aperture is assumed to be fed by a cylindrical transmission line. The electromagnetic (EM) fields inside the cavity are obtained using FEM. The EM fields and their normal derivatives required for FEM solution are obtained using (1) the modal expansion in the feed region and (2) the MoM for the radiating aperture region(assuming an infinite ground plane). The finiteness of the ground plane is taken into account using GTD. The input admittance of open ended circular, rectangular, and coaxial line radiating into free space through an infinite ground plane are computed and compared with earlier published results. Radiation characteristics of a coaxial cavity fed circular aperture in a finite rectangular ground plane are verified with experimental results.

Reddy, C. J.↗

DOE OSTI2022

A Multi-Scale Computational Platform for Predictive Modeling of Corrosion in Al-Steel Joints (Final Report)

The research team proposed to develop innovative multi-scale models to predict corrosion and the resulting mechanical performances in aluminum-steel joints. The methods of joining considered are resistance spot welding, self-piercing riveting, and rivet-welding, all suitable for mass production applications. The multi-scale models integrate high throughput first-principle calculations based on density functional theory (DFT), high throughput calculation of phase diagrams (CALPHAD) modeling, and finite element method (FEM) simulations. These models are to be validated through laboratory experiments. Furthermore, the models are available as open source so as to enable scientists and engineers in the community to adapt and contribute to the development and application. The approaches rely on the research team’s extensive experience on the prediction of properties of individual phases at finite temperatures and variable compositions through DFT calculations, and our broad expertise on dissimilar material joining and their corrosion. The proposed computational framework enables high throughput computations for improved predictions of corrosion and the associated mechanical performance in dissimilar material joints, resulting in significant reduction in computational time needed by the current state-of-the-art methods. With the participation of researchers from three universities, an auto manufacturer, two manufacturing technology/equipment suppliers, and a software developer/vendor, the interdisciplinary research team applies the technical development on both phase-based modeling and laboratory experiments into the automobile body joining processes for validation and technology demonstration. The global cost of corrosion was estimated at about 3.4% of the global GDP in 2013. By using available corrosion control practices, it is estimated a saving between 15-35% of the cost of corrosion. In the U.S., more than $276 billion is spent repairing corrosion damage. Prediction of the corrosion and its impact on performance of the dissimilar material joints is critical for reducing the massive number of the current corrosion-based recalls for automobiles. Thus, the project goal is to develop models to enable predictive maintenance and end-of-life planning of multi-metal joints with risk of corrosion under different conditions such as exposure to high temperatures in summer and salt solutions in winter, quantified through its pH. An academia-industry consortium led by the University of Michigan and including Pennsylvania State University, University of Illinois Urbana-Champaign, University of Georgia, General Motors Company, Livermore Software Technology Corporation, and Optimal Process Technologies, LLC. created multi-scale models for prediction of corrosion in aluminum-steel joint structures such of them used in vehicle subassemblies – chassis and transmission systems. Starting from the first principle calculations, the team developed mathematical and data-driven models to predict the metallic components, which are formed during joining of two metals, for example aluminum and steel - a lightweight multilateral system which is currently used in more than 60% car bodies. These models were used for simulating chemical reactions that are happening when the joining metallic components are exposed to high temperatures and different pH values. The team was able to predict how the corrosion installs on the metallic components and how they lead to a sudden failure of components in cars. Newly developed machine learning algorithms combining Science, Technology, Engineering and Math disciplines, advanced finite element simulation and experimental validations have been integrated in a platform for prediction of the corrosion evolution and prediction the failure of joints under mechanical loadings and fatigue. Moreover, based on machine learning and inverse analysis, the team proposed solutions for designing new metallic alloys less susceptible to corrosion when joining multi-material assembles. An average of 4% error compared with experiments was achieved for the most common joints that are used in vehicle subassemblies.

36 MATERIALS SCIENCE↗

NASA NTRS1994

A case study of analysis methods for large deflections of a cantilever beam

A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.

Craig, L. D.↗

NASA NTRS1978

A Special Purpose Architecture for Finite Element Analysis

The analysis of aerospace structures by the finite element method consumes considerable computer time. The cost of this resource and the designer's desire to have rapid feedback concerning such questions as the effect of a change in loading of the structure or in a parameter of some structural material led to the design of a special purpose parallel computing system for finite element analysis. As a special purpose computer, the architecture of this finite element computer is closely tied to computational aspects of the particular problem. Various aspects of an MIMD array of microprocessors are related to the requirements of the class of finite element analysis problems which it is intended to solve.

Jordan, H. F.↗

DOE OSTI2023

Calculation fo the Reflection and Transmission Coefficients for Gradual Tapered Waveguide Structures

It is required to find the reflection and transmission coefficients for a tapered waveguide. It is assumed that the taper is very long and gradual such that no higher order modes are excited from the discontinuity of the waveguide. Three different methods are presented for finding the reflection coefficient and two methods are presented for finding the transmission coefficient. A traditional differential equation method which finds only the reflection coefficient is presented. An additional set of differential equations are presented which finds both the reflection and transmission coefficients. A FEM (finite element method), which solves for both the reflection and transmission coefficients, is presented with its limitations. An example of a tapered coaxial line and waveguide is presented with the different methods compared and contrasted.

43 PARTICLE ACCELERATORS↗

NASA NTRS1984

Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.

Rosen, M. C.↗

NASA NTRS1985

Dynamic fracture mechanics

Dynamic fracture and crack propagation concepts for ductile materials are reviewed. The equations for calculating dynamic stress integrity and the dynamic energy release rate in order to study dynamic crack propagation are provided. The stress intensity factor versus crack velocity relation is investigated. The uses of optical experimental techniques and finite element methods for fracture analyses are described. The fracture criteria for a rapidly propagating crack under mixed mode conditions are discussed; crack extension and fracture criteria under combined tension and shear loading are based on maximum circumferential stress or energy criteria such as strain energy density. The development and use of a Dugdale model and finite element models to represent crack and fracture dynamics are examined.

Kobayashi, A. S.↗

NASA NTRS1994

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗

NASA NTRS1993

A Hybrid Symmetric FEM/MOM Formulation Applied to Scattering by Inhomogeneous Bodies of Revolution

A new symmetric formulation of the Hybrid Finite Element Method (HFEM) is described which combines elements of the Electric Field Integral Equation (EFIE) and the Magnetic Field Integral Equation (MFIE) for the exterior region along with the finite element solution for the interior problem. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfield radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions.

Lee, J-F.↗

NASA NTRS1991

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system components

This annual report summarizes the work completed during the third year of technical effort on the referenced contract. Principal developments continue to focus on the Probabilistic Finite Element Method (PFEM) which has been under development for three years. Essentially all of the linear capabilities within the PFEM code are in place. Major progress in the application or verifications phase was achieved. An EXPERT module architecture was designed and partially implemented. EXPERT is a user interface module which incorporates an expert system shell for the implementation of a rule-based interface utilizing the experience and expertise of the user community. The Fast Probability Integration (FPI) Algorithm continues to demonstrate outstanding performance characteristics for the integration of probability density functions for multiple variables. Additionally, an enhanced Monte Carlo simulation algorithm was developed and demonstrated for a variety of numerical strategies.

Source record↗

NASA NTRS1993

High temperature composite analyzer (HITCAN) user's manual, version 1.0

This manual describes 'how-to-use' the computer code, HITCAN (HIgh Temperature Composite ANalyzer). HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. This code combines composite mechanics and laminate theory with an internal data base for material properties of the constituents (matrix, fiber and interphase). The thermo-mechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress and stress rate. The computation procedure for the analysis of the composite structures uses the finite element method. HITCAN is written in FORTRAN 77 computer language and at present has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers. This manual describes HlTCAN's capabilities and limitations followed by input/execution/output descriptions and example problems. The input is described in detail including (1) geometry modeling, (2) types of finite elements, (3) types of analysis, (4) material data, (5) types of loading, (6) boundary conditions, (7) output control, (8) program options, and (9) data bank.

Lackney, J. J.↗

DOE OSTI2023

Residual Stresses Affect Cell Fragment Movement

Predictive modeling tools such as the finite element method can be of tremendous help in assessing the reliability and long-term performance of photovoltaic modules. In order to obtain accurate results, the proper modeling of materials and manufacturing processes are of utmost importance. Module fabrication introduces thermo-mechanical stresses inside the module laminate, which need to be accounted for as residual stresses in finite element simulations. We found that cell fragment movement and crack opening displacements of fractured silicon cells within modules are affected by those residual stresses. Cell cracking remains a challenging topic in assessing the reliability and durability of damaged modules. Hence, accurately quantifying the separation and movement between cell fragments creates the foundation for establishing reliable lifetime and performance assessments of fractured silicon modules. Here, we present a modeling approach that uses upper and lower bounds to accurately account for the residual stresses introduced by the module lamination process. We designed a four-point flexure coupon test of a laminated, fractured silicon strip to validate our numerical results and found good agreement between our modeling methodology and the experimental data. Finally, we discuss the implications of the residual stresses on the normal crack opening and metallization wear-out of fractured silicon cells.

14 SOLAR ENERGY↗

NASA NTRS2014

Strain Gage Load Calibration of the Wing Interface Fittings for the Adaptive Compliant Trailing Edge Flap Flight Test

The safety-of-flight parameters for the Adaptive Compliant Trailing Edge (ACTE) flap experiment require that flap-to-wing interface loads be sensed and monitored in real time to ensure that the structural load limits of the wing are not exceeded. This paper discusses the strain gage load calibration testing and load equation derivation methodology for the ACTE interface fittings. Both the left and right wing flap interfaces were monitored; each contained four uniquely designed and instrumented flap interface fittings. The interface hardware design and instrumentation layout are discussed. Twenty-one applied test load cases were developed using the predicted in-flight loads. Pre-test predictions of strain gage responses were produced using finite element method models of the interface fittings. Predicted and measured test strains are presented. A load testing rig and three hydraulic jacks were used to apply combinations of shear, bending, and axial loads to the interface fittings. Hardware deflections under load were measured using photogrammetry and transducers. Due to deflections in the interface fitting hardware and test rig, finite element model techniques were used to calculate the reaction loads throughout the applied load range, taking into account the elastically-deformed geometry. The primary load equations were selected based on multiple calibration metrics. An independent set of validation cases was used to validate each derived equation. The 2-sigma residual errors for the shear loads were less than eight percent of the full-scale calibration load; the 2-sigma residual errors for the bending moment loads were less than three percent of the full-scale calibration load. The derived load equations for shear, bending, and axial loads are presented, with the calculated errors for both the calibration cases and the independent validation load cases.

Miller, Eric J.↗

NASA NTRS1981

An adaptive, multi-level method for elliptic boundary value problems

Subroutine PLTMG is a FORTRAN program for solving self-adjoint elliptic boundary value problems in general regions of R-squared. It is based on a piecewise linear triangle finite element method, an adaptive grid refinement procedure, and a multi-level iterative method to solve the resulting sets of linear equations. This paper describes the method and presents some numerical results and comparisons.

Bank, R. E.↗

DOE OSTI2025

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗

DOE OSTI2026

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Trends and techniques for space base electronics

A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.

Gassaway, J. D.↗