Search NASASearch

SEARCH · Search NASA

Results for “Discrete 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 91 records · Page 5

Particle-Based Fiber Models of Woven Materials for Earth Entry Thermal Protection

Applications requiring materials with layer-to-layer strength, from basketry to thermal protection systems, use interlaced, three-dimensional woven materials. NASA is developing and deploying woven material heat shields for missions, including Artemis I (3D-MAT for compression pads) and potentially Mars Sample Return - Earth Entry System. These materials are complex, hierarchical and must protect from extreme environments and phenomena, such as deformation, impact and high-enthalpy heating. Woven material performance depends on microstructure, damage and weave geometry. Therefore, fiber-specific models are needed to simulate fiber contacts within the weave hierarchical geometry (fiber to tow to yarn to weave) and the inherent directionality of fibers. Explicit fiber models can simulate how weave microstructure evolution affects thermal and mechanical properties. We parameterize a discrete element bonded particle models (DEM-BPM) of fibers to capture thermal and mechanical behavior within and between fibers, with bonded and contact forces, respectively. We study the proportion of heat transfer and stress via the contact network, fiber bonds and the weave geometry, for example, with respect to yarn warp-weft identity (whether it interlaces weave layers). Our results demonstrate the importance of explicit fiber modeling for connecting microstructure with thermal and mechanical properties.

woven material

Particle-Based Fiber Models of Woven Materials for Earth Entry Thermal Protection

Applications requiring materials with layer-to-layer strength, from basketry to thermal protection systems, use interlaced, three-dimensional woven materials. NASA is developing and deploying woven material heat shields for missions, including Artemis I (3D-MAT for compression pads) and potentially Mars Sample Return - Earth Entry System. These materials are complex, hierarchical and must protect from extreme environments and phenomena, such as deformation, impact and high-enthalpy heating. Woven material performance depends on microstructure, damage and weave geometry. Therefore, fiber-specific models are needed to simulate fiber contacts within the weave hierarchical geometry (fiber to tow to yarn to weave) and the inherent directionality of fibers. Explicit fiber models can simulate how weave microstructure evolution affects thermal and mechanical properties. We parameterize a discrete element bonded particle models (DEM-BPM) of fibers to capture thermal and mechanical behavior within and between fibers, with bonded and contact forces, respectively. We study the proportion of heat transfer and stress via the contact network, fiber bonds and the weave geometry, for example, with respect to yarn warp-weft identity (whether it interlaces weave layers). Our results demonstrate the importance of explicit fiber modeling for connecting microstructure with thermal and mechanical properties.

woven material

High-performance finite elements with MFEM

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. Furthermore, this paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).

97 MATHEMATICS AND COMPUTING

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE

Methods for analysis of cracks in three-dimensional solids

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Raju, I. S.

A multigrid method for the transonic full potential equation discretized with finite elements on an arbitrary body fitted mesh

A multigrid method for the acceleration of transonic potential flow calculations based on a Galerkin finite element approach is described. In order to allow the use of arbitrary body fitted meshes it is necessary to introduce nonuniform interpolation and residual weighting. Emphasis is put on the construction of these operators consistent with the finite element approximation, while standard successive line overrelaxation is used as a smoothing step. Substantial convergence acceleration is obtained and results are presented for different transonic flow configurations including shocks.

Deconinck, H.

Application of the Finite Element Method to Rotary Wing Aeroelasticity

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Straub, F. K.

Unstructured Adaptive Meshes: Bad for Your Memory?

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Biswas, Rupak

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.

Correction factory techniques for improving aerodynamic prediction methods

A method for correcting discrete element lifting surface theory to reflect given experimental data is presented. Theoretical pressures are modified such that imposed constraints are satisfied while minimizing the changes to the pressures. Several types of correction procedures are presented and correlated; (1) scaling of pressures; (2) scaling of downwash values; and (3) addition of an increment to the downwash that is proportioned to pressure. Some special features are included in these methods and they include: (1) consideration of experimental data from multiple deflection modes, (2) limitation of the amplitudes of the correction factors, and (3) the use of correction factor mode shapes. These methods are correlated for cases involving all three Mach Number ranges using a FORTRAN IV computer program. Subsonically, a wing with an oscillating partial span control surface and a wing with a leading edge droop are presented. Transonically a two-dimensional airfoil with an oscillating flap is considered. Supersonically an arrow wing with and without camber is analyzed. In addition to correction factor methods an investigation is presented dealing with a new simplified transonic modification of the two-dimensional subsonic lifting surface theory. Correlations are presented for an airfoil with an oscillating flap.

Giesing, J. P.

Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.

97 MATHEMATICS AND COMPUTING

Nonlinear finite element formulation for the large displacement analysis in multibody system dynamics

A total Lagrangian finite element formulation for the deformable bodies in multibody mechanical systems that undergo finite relative rotations is developed. The deformable bodies are discretized using finite element methods. The shape functions that are used to describe the displacement field are required to include the rigid body modes that describe only large translational displacements. This does not impose any limitations on the technique because most commonly used shape functions satisfy this requirement. The configuration of an element is defined using four sets of coordinate systems: Body, Element, Intermediate element, Global. The body coordinate system serves as a unique standard for the assembly of the elements forming the deformable body. The element coordinate system is rigidly attached to the element and therefore it translates and rotates with the element. The intermediate element coordinate system, whose axes are initially parallel to the element axes, has an origin which is rigidly attached to the origin of the body coordinate system and is used to conveniently describe the configuration of the element in undeformed state with respect to the body coordinate system.

Rismantab-Sany, J.

Convergence of a Substructuring Method with LaGrange Multipliers

We analyze the convergence of a substructuring iterative method with Lagrange multipliers, proposed recently by Farhat and Roux. The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains and a coarse problem for the subdomain nullspace components. For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains, we prove the asymptotic bound on the condition number C(1 + log(H/h))(sup gamma), gamma = 2 or 3, where h is the characteristic element size and H is the subdomain size.

Mandel, Jan

Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.

Hull, P. V.

Error analysis of finite element solutions for postbuckled cylinders

A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.

Sistla, Rajaram

Methods for analysis of cracks in three-dimensional solids

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Raju, I. S.

Ablative Thermal Response Analysis Using the Finite Element Method

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.

Dec John A.