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At least 1,603 records · Page 89

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NASA NTRS1992

An improved plate theory of order (1,2) for thick composite laminates

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.

Tessler, A.↗

NASA NTRS1997

Numerical Study of Magnetic Damping During Unidirectional Solidification

A fully 3-D numerical model is developed to represent magnetic damping of complex fluid flow, heat transfer and electromagnetic field distributions in a melt cavity. The model is developed based on our in-house finite element code for the fluid flow, heat transfer and electromagnetic field calculations. The computer code has been tested against benchmark test problems that are solved by other commercial codes as well as analytical solutions whenever available. The numerical model is tested against numerical and experimental results for water reported in literature. With the model so tested, various numerical simulations are carried out for the Sn-35.5% Pb melt convection and temperature distribution in a cylindrical cavity with and without the presence of a transverse magnetic field. Numerical results show that magnetic damping can be effectively applied to reduce turbulence and flow levels in the melt undergoing solidification and over a certain threshold value a higher magnetic field resulted in a higher velocity reduction. It is found also that for a fully 3-D representation of the magnetic damping effects, the electric field induced in the melt by the applied DC magnetic field does not vanish, as some researchers suggested, and must be included even for molten metal and semiconductors. Also, for the study of the melt flow instability, a long enough time has to be applied to ensure the final fluid flow recirculation pattern. Moreover, our numerical results suggested that there seems to exist a threshold value of applied magnetic field, above which magnetic damping becomes possible and below which the convection in the melt is actually enhanced. Because of the limited financial resource allocated for the project, we are unable to carry out extensive study on this effect, which should warrant further theoretical and experimental study. In that endeavor, the developed numerical model should be very useful; and the model should serve as a useful tool for exploring necessary design parameters for planning magnetic damping experiments and interpreting the experimental results.

Li, Ben Q.↗

NASA NTRS2002

A Discontinuous Galerkin Discretization of the Eikonal Equation on Curved Piecewise Isoparametric Triangulated Manifolds

This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.

Barth, TIm↗

NASA NTRS2007

Application of the Finite Element Method in Atomic and Molecular Physics

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Shertzer, Janine↗

DOE OSTI2016

Fracture Network and Fluid Flow Imaging for Enhanced Geothermal Systems Applications from Multi-Dimensional Electrical Resistivity Structure

We have developed an algorithm for the inversion of magnetotelluric (MT) data to a 3D earth resistivity model based upon the finite element method. Hexahedral edge finite elements are implemented to accommodate discontinuities in the electric field across resistivity boundaries, and to accurately simulate topographic variations. All matrices are reduced and solved using direct solution modules which avoids ill-conditioning endemic to iterative solvers such as conjugate gradients, principally PARDISO for the finite element system and PLASMA for the parameter step estimate. Large model parameterizations can be handled by transforming the Gauss-Newton estimator to data-space form. Accuracy of the forward problem and jacobians has been checked by comparison to integral equations results and by limiting asymptotes. Inverse accuracy and performance has been verified against the public Dublin Secret Test Model 2 and the well-known Mount St Helens 3D MT data set. This algorithm we believe is the most capable yet for forming 3D images of earth resistivity structure and their implications for geothermal fluids and pathways.

15 GEOTHERMAL ENERGY↗

DOE OSTI2017

An algebraic multigrid method for Q 2 - Q 1 mixed discretizations of the Navier-Stokes equations: AMG for Q 2 - Q 1 discretization

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily colocated at mesh points. Specifically, we investigate a Q 2 -Q 1 mixed finite element discretization of the incompressible Navier–Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees of freedom (DOFs) are defined at spatial locations where there are no corresponding pressure DOFs. Thus, AMG approaches leveraging this colocated structure are not applicable. This article instead proposes an automatic AMG coarsening that mimics certain pressure/velocity DOF relationships of the Q 2 -Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity DOFs resembles that on the finest grid. To define coefficients within the intergrid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier–Stokes problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Contact pressure analysis to allow improved design for the clearing plate in a biomass comminution system

For biomass processing systems, feedstocks with small but equal sizes can improve flowability and thermochemical outputs. The Crumbler rotary shear system was designed to achieve such ideal feedstocks to reduce costs and energy throughout the biomass supply chain. Improving the wear resistance of major components in this system is important to decrease the cost. Accelerating the feedstock flow through the rotary shear machine plays an equivalent role of improving its efficiency. An analytical analysis and a finite-element analysis of the stationary clearing plate are presented in this work. Here, these tools are used to investigate the effect of contact surface curvature on the impact pressure. The optimized new clearing plate design is expected to improve the component’s lifetime and wood chips flowability. The field tests confirm that the trend of the new clearing plate design guided by FEA. The optimization method, model verification, and validation experience applied in this work can also be applied to other static components with similar simple contact wear problems.

09 BIOMASS FUELS↗

NASA NTRS1999

Crack Growth Simulation and Residual Strength Prediction in Airplane Fuselages

This is the final report for the NASA funded project entitled "Crack Growth Prediction Methodology for Multi-Site Damage." The primary objective of the project was to create a capability to simulate curvilinear fatigue crack growth and ductile tearing in aircraft fuselages subjected to widespread fatigue damage. The second objective was to validate the capability by way of comparisons to experimental results. Both objectives have been achieved and the results are detailed herein. In the first part of the report, the crack tip opening angle (CTOA) fracture criterion, obtained and correlated from coupon tests to predict fracture behavior and residual strength of built-up aircraft fuselages, is discussed. Geometrically nonlinear, elastic-plastic, thin shell finite element analyses are used to simulate stable crack growth and to predict residual strength. Both measured and predicted results of laboratory flat panel tests and full-scale fuselage panel tests show substantial reduction of residual strength due to the occurrence of multi-site damage (MSD). Detailed comparisons of n stable crack growth history, and residual strength between the predicted and experimental results are used to assess the validity of the analysis methodology. In the second part of the report, issues related to crack trajectory prediction in thin shells; an evolving methodology uses the crack turning phenomenon to improve the structural integrity of aircraft structures are discussed, A directional criterion is developed based on the maximum tangential stress theory, but taking into account the effect of T-stress and fracture toughness orthotropy. Possible extensions of the current crack growth directional criterion to handle geometrically and materially nonlinear problems are discussed. The path independent contour integral method for T-stress evaluation is derived and its accuracy is assessed using a p- and hp-version adaptive finite element method. Curvilinear crack growth is simulated in coupon tests and in full-scale fuselage panel tests. Both T-stress and fracture toughness orthotropy are found to be essential to predict the observed crack paths. The analysis methodology and software program (FRANC3D/STAGS) developed herein allows engineers to maintain aging aircraft economically while insuring continuous airworthiness. Consequently, it will improve the technology to support the safe operation of the current aircraft fleet as well as the design of more damage-tolerant aircraft for the next generation fleet.

Chen, Chuin-Shan↗

NASA NTRS1983

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques and a problem adaptive computational algorithm are presented for predicting the nonlinear steady state temperature distribution in structures and solids. In the proposed techniques, the structure is discretized by using the finite element method. The vector of nodal temperatures is then expressed as a linear combination of a small number of global temperature modes (or basis vectors), and the Bubnov Galerkin technique is used to compute the amplitudes of the global modes. The global temperature modes (or basis vectors) are chosen to include the various order derivatives of the nodal temperature vector with respect to preselected path parameter(s). The potential of the proposed reduction methods for solution of large scale, nonlinear thermal problems is discussed and the effectiveness of the methods is demonstrated by means of numerical examples, including steady state conduction, convection, and radiation modes of heat transfer.

Noor, A. K.↗

NASA NTRS1983

Structural optimization by multilevel decomposition

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1976

Analysis of transonic flow over lifting and oscillating airfoils

Finite element procedures are presented for the numerical solution of transonic flow over lifting and oscillating airfoils based on small disturbance theory. The algorithm is simple and effective in handling the mixed flow problem and, for airfoil in free air, treats the entire flow domain by making use of the far field asymptotic solution. Numerical results are presented and compared with experimental data and those obtained by finite difference relaxation techniques.

Chan, S. T. K.↗

NASA NTRS1993

Hybrid techniques for complex aerospace electromagnetics problems

Important aerospace electromagnetics problems include the evaluation of antenna performance on aircraft and the prediction and control of the aircraft's electromagnetic signature. Due to the ever increasing complexity and expense of aircraft design, aerospace engineers have become increasingly dependent on computer solutions. Traditionally, computational electromagnetics (CEM) has relied primarily on four disparate techniques: the method of moments (MoM), the finite-difference time-domain (FDTD) technique, the finite element method (FEM), and high frequency asymptotic techniques (HFAT) such as ray tracing. Each of these techniques has distinct advantages and disadvantages, and no single technique is capable of accurately solving all problems of interest on computers that are available now or will be available in the foreseeable future. As a result, new approaches that overcome the deficiencies of traditional techniques are beginning to attract a great deal of interest in the CEM community. Among these new approaches are hybrid methods which combine two or more of these techniques into a coherent model. During the ASEE Summer Faculty Fellowship Program a hybrid FEM/MoM computer code was developed and applied to a geometry containing features found on many modern aircraft.

Aberle, Jim↗

NASA NTRS1989

Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states.

Yae, K. Harold↗

DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

A hybrid finite element-spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

The finite element method (FEM) and the spectral boundary integral method (SBI) have both been widely used in the study of dynamic rupture simulations along a weak interface. Here, we present a hybrid method that combines FEM and SBI through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small-scale heterogeneities and from the superior performance and accuracy of SBI. We validate the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises.We further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off-fault heterogeneities by studying a 2D in-plane shear crack in two different settings: one where the crack is embedded in a high-velocity zone and another where it is embedded in a low-velocity zone. Finally, we discuss the potential of the hybrid method for addressing a wide range of problems in geophysics and engineering.

58 GEOSCIENCES↗

NASA NTRS1984

Quasi-static solution algorithms for kinematically/materially nonlinear thermomechanical problems

This paper develops an algorithmic solution strategy which allows the handling of positive/indefinite stiffness characteristics associated with the pre- and post-buckling of structures subject to complex thermomechanical loading fields. The flexibility of the procedure is such that it can be applied to both finite difference and element-type simulations. Due to the generality of the algorithmic approach developed, both kinematic and thermal/mechanical type material nonlinearity including inelastic effects can be treated. This includes the possibility of handling completely general thermomechanical boundary conditions. To demonstrate the scheme, the results of several benchmark problems is presented.

Padovan, J.↗

NASA NTRS1993

An analytical/numerical correlation study of the multiple concentric cylinder model for the thermoplastic response of metal matrix composites

The utility of a recently developed analytical micromechanics model for the response of metal matrix composites under thermal loading is illustrated by comparison with the results generated using the finite-element approach. The model is based on the concentric cylinder assemblage consisting of an arbitrary number of elastic or elastoplastic sublayers with isotropic or orthotropic, temperature-dependent properties. The elastoplastic boundary-value problem of an arbitrarily layered concentric cylinder is solved using the local/global stiffness matrix formulation (originally developed for elastic layered media) and Mendelson's iterative technique of successive elastic solutions. These features of the model facilitate efficient investigation of the effects of various microstructural details, such as functionally graded architectures of interfacial layers, on the evolution of residual stresses during cool down. The available closed-form expressions for the field variables can readily be incorporated into an optimization algorithm in order to efficiently identify optimal configurations of graded interfaces for given applications. Comparison of residual stress distributions after cool down generated using finite-element analysis and the present micromechanics model for four composite systems with substantially different temperature-dependent elastic, plastic, and thermal properties illustrates the efficacy of the developed analytical scheme.

Pindera, Marek-Jerzy↗