Search NASA⌕ Search

SEARCH · Search NASA

Results for “finite element Method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,423 records · Page 79

Predicting Deformation Limits of Dual-Phase Steels Under Complex Loading Paths

The deformation limits of various DP980 steels are examined in this study with deformation instability theory. Under uniaxial tension, overall stress-strain curves of the material are estimated based on simple rule of mixture (ROM) with both iso-strain and iso-stress assumptions. Under complex loading paths, actual microstructure-based finite element (FE) method is used to explicitly resolve the deformation incompatibilities between the soft ferrite and hard martensite phases. The results show that, for uniaxial tension, the deformation instability theory with iso-strain-based ROM can be used to provide the lower bound estimate of the uniform elongation (UE) for the various DP980 considered. Under complex loading paths, the deformation instability theory with microstructure-based FE method can be used in examining the effects of various microstructural features on the deformation limits of DP980 steels.

36 MATERIALS SCIENCE↗

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

97 MATHEMATICS AND COMPUTING↗

Ultrasonic guided waves in eccentric annular pipes

This paper studies the feasibility of using ultrasonic guided waves to rapidly inspect tubes and pipes for possible eccentricity. While guided waves are well established in the long range inspection of structures such as pipes and plates, studies for more complex cross sections are limited and analytical solutions are often difficult to obtain. Recent developments have made the Semi Analytical Finite Element (SAFE) method widely accessible for researchers to study guided wave properties in complex structures. Here the SAFE method is used to study the effect of eccentricity on the modal structures and velocities of lower order guided wave modes in thin pipes of diameters typically of interest to the industry. Results are validated using experiments. The paper demonstrates that even a small eccentricity in the pipe can strongly affect guided wave mode structures and velocities and hence shows potential for pipe eccentricity inspection.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

PROTEUS-MOC User Manual

The PROTEUS-MOC code is a three-dimensional (3D) neutron transport code based on the finite element mesh and the method of characteristics (MOC) which combines a 2D MOC with the discontinuous Galerkin finite element method for the axial direction. Thus, for PROTEUS-MOC, a 3D geometry is represented with by the implicit extrusion of a single 2D planar geometry with different material assignments allowable on each plane. The code requires four input files for a steady-state calculation without the thermal feedback: a driver input, a mesh input, a cross section input, and a material assignment input. With thermal feedback, a T/H input file is needed. For kinetics, a kinetics driver input file is required. The PROTEUS-MOC software produces a text output file as well as a data file which includes integral and average quantities such on fluxes, powers, temperatures, densities, etc. The detailed output file can be converted to the VTK format using the post processing code so that the outputs can be visualized using a visualization software such as VisIt.

97 MATHEMATICS AND COMPUTING↗

Selective growth of Ni4Ti3 precipitate variants induced by complicated cyclic stress during laser additive manufacturing of NiTi-based composites

Highlights: • The NiTi-based composites were in-situ synthesized by SLM. • Ni{sub 4}Ti{sub 3} could tailor the phase transformation temperature of TiC/NiTi composites. • A three-dimensional stress field modeling of TiC/NiTi composites was established. • The relationship between growth of Ni{sub 4}Ti{sub 3} variants and cyclic stress was disclosed. - Abstract: NiTi-based composites were in-situ synthesized by selective laser melting (SLM) additive manufacturing technology with formation of a great many Ni{sub 4}Ti{sub 3} precipitates. The differential scanning calorimetry (DSC) were carried out to exhibit the similar phase transformation temperature (A{sub s} = 51.82 °C, A{sub f} = 94.02 °C, M{sub s} = 55.87 °C and M{sub f} = 18.93 °C) by comparing with that of SLM-fabricated equi-atomic NiTi alloy, which could be attributed to the compensation of Ni{sub 4}Ti{sub 3} precipitates for the effect of an addition of TiC particles. Three different Ni{sub 4}Ti{sub 3} precipitate variants ((111){sub R}//(1 1-bar 1-bar ){sub B2}, (111){sub R}//( 1-bar 1-bar 1){sub B2}, and (111){sub R}//( 1-bar 1 1-bar ){sub B2}) with various precipitate diameters were observed within SLM fabricated part, showing apparently selective growth behavior. By high-resolution transmission electron microscopy, severe lattice defects formed surrounding the smaller variant, while relatively intact lattice structure was found around the larger one, which indicated that high strain energy was produced in the interface between the matrix and the smaller variant. Furthermore, finite element simulation method was applied to disclose the evolution features of complicated cyclic stress during SLM processing of TiC/NiTi composites. By predicting, the main constraint mode within as-fabricated track was tensile stress effect. Based on the redistribution behavior of thermal stress and the coupling effect between the thermal stress and strain field induced by Ni{sub 4}Ti{sub 3} precipitate, the selective growth mechanism of Ni{sub 4}Ti{sub 3} variant was revealed.

36 MATERIALS SCIENCE↗

Scattering of plane guided waves obliquely incident on straight features

A semi-analytical finite element model is developed to study the scattering of plane guided waves obliquely incident on a straight geometric feature. The model is first used to investigate the reflection of the S0 mode from a free edge and the results are compared to those of bulk waves reflecting from a free boundary. The model is then used to predict the transmission of the S0 mode past an adhesively-bonded stiffener. The results obtained are in excellent agreement with experimental measurements.

42 ENGINEERING↗

A Modified Isotropic–Kinematic Hardening Model to Predict the Defects in Tube Hydroforming Process

Numerical simulations of tube hydroforming process of hollow crankshafts were conducted by using finite element analysis method. Moreover, the modified model involving the integration of isotropic–kinematic hardening model with ductile criteria model was used to more accurately optimize the process parameters such as internal pressure, feed distance and friction coefficient. Subsequently, hydroforming experiments were performed based on the simulation results. The comparison between experimental and simulation results indicated that the prediction of tube deformation, crack and wrinkle was quite accurate for the tube hydroforming process. Finally, hollow crankshafts with high thickness uniformity were obtained and the thickness distribution between numerical and experimental results was well consistent.

36 MATERIALS SCIENCE↗

Deformation heterogeneity and intragrain lattice misorientation in high strength contrast, dual-phase bridgmanite/periclase

A bridgmanite/periclase aggregate is investigated due to its prevalence in the Earth’s lower mantle and its importance for understanding geodynamic processes. In dual-phase polycrystalline aggregates, both strength contrast between phases and single crystal elastic and plastic anisotropy are known to influence the development of intragrain misorientation, and the evolution of crystallographic texture. In this study, full-field crystal plasticity simulations are performed with a finite element solution method, and applied to an aggregate of a mechanically strong orthorhombic phase with perovskite structure (bridgmanite, MgSiO 3 ), and a relatively weaker cubic phase (periclase, MgO). The relative strengths of the phases are parameterized to elucidate the effect that strength contrast has on texture evolution and single-phase simulations are performed for comparison. Altogether, results indicate that the relative strength between the two phases influences the development of plasticity, and the overall texture evolution. Results are discussed in light of trends related to the evolution of plasticity and misorientation in the aggregate, and their dependence on both the strength contrast between phases as well as the spatial distribution of grains and phases.

36 MATERIALS SCIENCE↗

SU-F-J-88: Comparison of Two Deformable Image Registration Algorithms for CT-To-CT Contour Propagation

Purpose: To compare the contour propagation accuracy of two deformable image registration (DIR) algorithms in the Raystation treatment planning system – the “Hybrid” algorithm based on image intensities and anatomical information; and the “Biomechanical” algorithm based on linear anatomical elasticity and finite element modeling. Methods: Both DIR algorithms were used for CT-to-CT deformation for 20 lung radiation therapy patients that underwent treatment plan revisions. Deformation accuracy was evaluated using landmark tracking to measure the target registration error (TRE) and inverse consistency error (ICE). The deformed contours were also evaluated against physician drawn contours using Dice similarity coefficients (DSC). Contour propagation was qualitatively assessed using a visual quality score assigned by physicians, and a refinement quality score (0 0.9 for lungs, > 0.85 for heart, > 0.8 for liver) and similar qualitative assessments (VQS < 0.35, RQS > 0.75 for lungs). When anatomical structures were used to control the deformation, the DSC improved more significantly for the biomechanical DIR compared to the hybrid DIR, while the VQS and RQS improved only for the controlling structures. However, while the inclusion of controlling structures improved the TRE for the hybrid DIR, it increased the TRE for the biomechanical DIR. Conclusion: The hybrid DIR was found to perform slightly better than the biomechanical DIR based on lower TRE while the DSC, VQS, and RQS studies yielded comparable results for both. The use of controlling structures showed considerable improvement in the hybrid DIR results and is recommended for clinical use in contour propagation.

60 APPLIED LIFE SCIENCES↗

Modelling grain-scattered ultrasound in austenitic stainless-steel welds: A hybrid model

The ultrasonic inspection of austenitic stainless steel welds can be challenging due to their coarse grain structure, charaterised by preferentially oriented, elongated grains. The anisotropy of the weld is manifested as both a ‘steering’ of the beam and the back-scatter of energy due to the macroscopic granular structure of the weld. However, the influence of weld properties, such as mean grain size and orientation distribution, on the magnitude of scattered ultrasound is not well understood. A hybrid model has been developed to allow the study of grain-scatter effects in austenitic welds. An efficient 2D Finite Element (FE) method is used to calculate the complete scattering response from a single elliptical austenitic grain of arbitrary length and width as a function of the specific inspection frequency. A grain allocation model of the weld is presented to approximate the characteristic structures observed in austenitic welds and the complete scattering behaviour of each grain calculated. This model is incorporated into a semi-analytical framework for a single-element inspection of a typical weld in immersion. Experimental validation evidence is demonstrated indicating excellent qualitative agreement of SNR as a function of frequency and a minimum SNR difference of 2 dB at a centre frequency of 2.25 MHz. Additionally, an example Monte-Carlo study is presented detailing the variation of SNR as a function of the anisotropy distribution of the weld, and the application of confidence analysis to inform inspection development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Energetic Galerkin BEM for 2D Wave Propagation Problems in Piecewise Homogeneous Media

We consider Dirichlet-Neumann problems for two-dimensional wave propagation analysis in piecewise homogeneous media reformulated in terms of boundary integral equations. The related weak problem is based on a space-time energetic formulation recently introduced for single-domain problems. The discretization phase is carried out by means of Galerkin boundary element method. Numerical results obtained with this procedure will be presented and analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Springback Analysis of Draw-Bending of 980 MPa Cold Rolled Steel Sheet and Its Experimental Validation

Draw-bending experiment is carried out using a 1.2 mm-thick high strength steel sheet with a tensile strength of 980 MPa and the residual curvature of the draw-bent specimens are precisely measured. The die profile of the draw-bending testing machine rotates, so that the effect of friction force on the curvature data after springback can be neglected. Moreover, in order to quantitatively evaluate the Bauschinger effect of the test material, stress reversal tests are performed using an in-plane stress reversal testing machine. Furthermore, the finite element analyses (FEA) of the draw-bending experiment are carried out. The effect of the work hardening models (isotropic or combined), element types (shell or solid), and the number of integration points in the through-thickness direction on the amount of springback (residual curvature) are investigated in detail.

36 MATERIALS SCIENCE↗

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

97 MATHEMATICS AND COMPUTING↗

A Study of Tube Extrusion Process

An upper bound solution for tube extrusion is developed in this paper. The dead zone is assumed to have the sine profile and a kinematically admissible velocity field is proposed. From the proposed velocity field, the upper bound solution on relative punch pressure and extrusion load is determined with respect to chosen process parameters. The results are compared with theoretical and experimental results from a reference to illustrate the validity of the proposed velocity field. This indicates that the analysis presented here renders better upper bound solution than that given by Ebrahimi et al.. [An upper-bound analysis of the tube extrusion process (2008) J. Mater. Process. Technol. 99:214-220].

42 ENGINEERING↗