Results for “boundary element method” — Page 65

DOE OSTI2021

SIERRA Multimechanics Module: Aria User Manual (Version.5.2)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.2)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.4)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.6)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( $Re$ < 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.6)

Aria is a Galerkin nite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

42 ENGINEERING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual - Version 5.8

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual - Version 5.8

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process ows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria User Manual (V.5.10)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ($Re$ < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.10)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ($Re$ < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

42 ENGINEERING↗

DOE OSTI2020

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.4.56)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

Optimal design of geodesically stiffened composite cylindrical shells

An optimization system based on the finite element code Computations Structural Mechanics (CSM) Testbed and the optimization program, Automated Design Synthesis (ADS), is described. The optimization system can be used to obtain minimum-weight designs of composite stiffened structures. Ply thickness, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells and shells stiffened by rings and stingers are also obtained. Trends in the design of geodesically stiffened shells are identified. An approach to include local stress concentrations during the design optimization process is then presented. The method is based on a global/local analysis technique. It employs spline interpolation functions to determine displacements and rotations from a global model which are used as 'boundary conditions' for the local model. The organization of the strategy in the context of an optimization process is described. The method is validated with an example.

Gendron, G.↗

NASA NTRS1994

A Method for Thermal Analysis of Spiral Bevel Gears

A modeling method for analyzing the three-dimensional thermal behavior of spiral bevel gears has been developed. The model surfaces are generated through application of differential geometry to the manufacturing process for face-milled spiral bevel gears. Contact on the gear surface is found by combining tooth contact analysis with three-dimensional Hertzian theory. The tooth contact analysis provides the principle curvatures and orientations of the two surfaces. This information is then used directly in the Hertzian analysis to find the contact size and maximum pressure. Heat generation during meshing is determined as a function of the applied load, sliding velocity, and coefficient of friction. Each of these factors change as the point of contact changes during meshing. A nonlinear finite element program was used to conduct the heat transfer analysis. This program permitted the time- and position-varying boundary conditions, found in operation, to be applied to a one-tooth model. An example model and analytical results are presented.

Handschuh, Robert F.↗

NASA NTRS2004

Reliability Quantification of the Flexure: A Critical Stirling Convertor Component

Uncertainties in the manufacturing, fabrication process, material behavior, loads, and boundary conditions results in the variation of the stresses and strains induced in the flexures and its fatigue life. Past experience and the test data at material coupon levels revealed a significant amount of scatter of the fatigue life. Owing to these facts, the design of the flexure, using conventional approaches based on safety factor or traditional reliability based on similar equipment considerations does not provide a direct measure of reliability. Additionally, it may not be feasible to run actual long term fatigue tests due to cost and time constraints. Therefore it is difficult to ascertain material fatigue strength limit. The objective of the paper is to present a methodology and quantified results of numerical simulation for the reliability of flexures used in the Stirling convertor for their structural performance. The proposed approach is based on application of finite element analysis method in combination with the random fatigue limit model, which includes uncertainties in material fatigue life. Additionally, sensitivity of fatigue life reliability to the design variables is quantified and its use to develop guidelines to improve design, manufacturing, quality control and inspection design process is described.

Shah, Ashwin R.↗

NASA NTRS2010

Vibration Response Predictions for Heavy Panel Mounted Components from Panel Acreage Environment Specifications

The development of new launch vehicles in the Aerospace industry often relies on response measurements taken from previously developed vehicles during various stages of liftoff and ascent, and from wind tunnel models. These measurements include sound pressure levels, dynamic pressures in turbulent boundary layers and accelerations. Rigorous statistical scaling methods are applied to the data to derive new environments and estimate the performance of new skin panel structures. Scaling methods have proven to be reliable, particularly for designs similar to the vehicles used as the basis for scaling, and especially in regions of smooth acreage without exterior protuberances or heavy components mounted to the panel. To account for response attenuation of a panel-mounted component due to its apparent mass at higher frequencies, the vibroacoustics engineer often reduces the acreage vibration according to a weight ratio first suggested by Barrett. The accuracy of the reduction is reduced with increased weight of the panel-mounted component, and does not account for low-frequency amplification of the component/panel response as a system. A method is proposed that combines acreage vibration from scaling methods with finite element analysis to account for the frequency-dependent dynamics of heavy panel-mounted components. Since the acreage and mass-loaded skins respond to the same dynamic input pressure, such pressure may be eliminated in favor of a frequency-dependent scaling function applied to the acreage vibration to predict the mass-loaded panel response. The scaling function replaces the Barrett weight ratio, and contains all of the dynamic character of the loaded and unloaded skin panels. The solution simplifies for spatially uncorrelated and fully correlated input pressures. Since the prediction uses finite element models of the loaded and unloaded skins, a rich suite of response data are available to the design engineer, including interface forces, stress and strain, as well as acceleration and displacement. An extension of the method is also developed to incorporate the effect of a local protuberance near a heavy component. Acreage environments from traditional scaling methods with and without protuberance effects serve as the basis for the extension. Authors:

Harrison, Phillip↗

NASA NTRS1991

Finite element computation of compressible flows with the SUPG formulation

Finite element computation of compressible Euler equations is presented in the context of the streamline-upwind/Petrov-Galerkin (SUPG) formulation. The SUPG formulation, which is based on adding stabilizing terms to the Galerkin formulation, is further supplemented with a shock capturing operator which addresses the difficulty in maintaining a satisfactory solution near discontinuities in the solution field. The shock capturing operator, which has been derived from work done in entropy variables for a similar operator, is shown to lead to an appropriate level of additional stabilization near shocks, without resulting in excessive numerical diffusion. An implicit treatment of the impermeable wall boundary condition is also presented. This treatment of the no-penetration condition offers increased stability for large Courant numbers, and accelerated convergence of the computations for both implicit and explicit applications. Several examples are presented to demonstrate the ability of this method to solve the equations governing compressible fluid flow.

Le Beau, G. J.↗

NASA NTRS1959

Vacuum-Induction, Vacuum-Arc, and Air-Induction Melting of a Complex Heat-Resistant Alloy

The relative hot-workability and creep-rupture properties at 1600 F of a complex 55Ni-20Cr-15Co-4Mo-3Ti-3Al alloy were evaluated for vacuum-induction, vacuum-arc, and air-induction melting. A limited study of the role of oxygen and nitrogen and the structural effects in the alloy associated with the melting process was carried out. The results showed that the level of boron and/or zirconium was far more influential on properties than the melting method. Vacuum melting did reduce corner cracking and improve surface during hot-rolling. It also resulted in more uniform properties within heats. The creep-rupture properties were slightly superior in vacuum heats at low boron plus zirconium or in heats with zirconium. There was little advantage at high boron levels and air heats were superior at high levels of boron plus zirconium. Vacuum heats also had fewer oxide and carbonitride inclusions although this was a function of the opportunity for separation of the inclusions from high oxygen plus nitrogen heats. The removal of phosphorous by vacuum melting was not found to be related to properties. Oxygen plus nitrogen appeared to increase ductility in creep-rupture tests suggesting that vacuum melting removes unidentified elements detrimental to ductility. Oxides and carbonitrides in themselves did not initiate microcracks. Carbonitrides in the grain boundaries of air heats did initiate microcracks. The role of microcracking from this source and as a function of oxygen and nitrogen content was not clear. Oxygen and nitrogen did intensify corner cracking during hot-rolling but were not responsible for poor surface which resulted from rolling heats melted in air.

Decker, R. F.↗

DOE OSTI2021

A 3D Full Stress Tensor Model for Oklahoma

Abstract The stress tensor is an important property for upper crustal studies such as those that involve pore fluids and earthquake hazards. At tectonic plate scale, plate boundary forces and mantle convection are the primary drivers of the stress field. In many local settings (10–100 s of km and <10 km depth) in tectonic plate interiors, we can simplify by assuming a constant background stress field that is perturbed by local heterogeneity in density and elasticity. Local stress orientation and sometimes magnitude can be estimated from earthquake and borehole‐based observations when available. Modeling of the local stress field often involves interpolating sparse observations. We present a new method to estimate the 3D stress field in the upper crust and demonstrate it for Oklahoma. We created a 3D material model by inverting multiple types of geophysical observations simultaneously. Integrating surface‐wave dispersion, local travel times and gravity observations produces a model of P‐wave velocity, S‐wave velocity, and density. The stress field can then be modeled using finite element simulations. The simulations are performed using our simplified view of the local stress field as the sum of a constant background stress field that is perturbed by local density and elasticity heterogeneity and gravitational body forces. An orientation of N82°E, for the maximum compressive tectonic force, best agrees with previously observed stress orientations and faulting types in Oklahoma. The gravitational contribution of the horizontal stress field has a magnitude comparable to the tectonic contribution for the upper 5 km of the subsurface.

58 GEOSCIENCES↗

NASA NTRS1989

Acoustic wave propagation in heterogeneous structures including experimental validation

A finite element model was developed to solve for the acoustic pressure and energy fields in a heterogeneous suppressor. The derivations from the governing equations assumed that the material properties could vary with position resulting in a heterogeneous variable property two-dimensional wave equation. This eliminated the necessity of finding the boundary conditions between different materials. For a two media region consisting of part air and part bulk absorber, a model was used to describe the bulk absorber properties in two directions. Complex metallic structures inside the air duct are simulated by simply changing element properties from air to the structural material in a pattern to describe the desired shapes. To verify the numerical theory, experiments were conducted without flow in a rectangular duct with a single folded cavity mounted above the duct and absorbing material mounted inside a cavity. Changes in a nearly plane wave sound field were measured on the wall opposite the absorbing cavity. Fairly good agreement was found in the standing wave pattern upstream of the absorber and in the decay of pressure level opposite the absorber, as a function of distance along the duct. The finite element model provides a convenient method for evaluating the acoustic properties of bulk absorbers.

Baumeister, Kenneth J.↗