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At least 487 records · Page 27

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NASA NTRS1993

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Chang, H. J.↗

NASA NTRS1985

Stability, accuracy, and efficiency of some underintegrated methods in finite element computations

In an attempt to increase computational efficiency in the numerical solution of highly nonlinear problems in solid and fluid mechanics, underintegrated finite element methods have been employed by many analysts. Underintegration refers to the use of a rule of an order lower than that required to integrate polynomial integrands exactly. The main drawback of this technique is related to the production of rank-deficient stiffness matrices, or equivalently an expanded kernel of the governing linear momentum operators. Such a development can introduce numerical instabilities. In order to overcome this difficulty, artificial stiffness or viscosity methods, or other stabilization methods have been proposed. One approach involves the elimination of spurious modes in a postprocessing operation. The present study is concerned with this a posteriori elimination method, taking into account the results which can be expected from it, and some of its possible extensions.

Jacquotte, O.-P.↗

NASA NTRS1973

The constraint method: A new finite element technique

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

Tsai, C.↗

NASA NTRS1992

Hierarchical flux-based thermal-structural finite element analysis method

A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.

Polesky, Sandra P.↗

DOE OSTI2023

Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

42 ENGINEERING↗

NASA NTRS1984

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.↗

NASA NTRS1979

Stress-intensity factors for internal surface cracks in cylindrical pressure vessels

The stress intensity factors were calculated by a three dimensional finite element method. The finite element models employed singularity elements along the crack front and linear strain elements elsewhere. The models had about 6500 degrees of freedom. The stress intensity factors were evaluated from a nodal force method. An equation for the stress intensity factors was obtained form the results of the present analysis. The equation applies over a wide range of configuration parameters and was within about 5 percent of the present results. A comparison was made between the present results and other analyses of internal surface cracks in cylinders. The results from a boundary integral equation method were in agreement (+ or - 2 percent) and those from another finite element were in fair agreement (+ or - 8 percent) with the present results.

Newman, J. C., Jr.↗

NASA NTRS1988

Finite element substructuring methods for composite mechanics

Finite element substructuring strategies are presented to obtain numerical solutions for three typical problems of interest to the composites community: (1) impact and toughness characterization of composites using Charpy's impact test specimen; (2) free-edge stress analysis of composite laminates; and (3) fracture toughness predictions of composites for individual and combined fracture of modes I, II, and III. The key issue common to these problems is the presence of singular or near singular stress fields. The regions prone to see steep stress gradients are substructured with progressively refined meshes to study the local response simultaneously with the global response. The results from the select examples indicate that finite element substructuring methods are computationally effective for composite singularity mechanics.

Murthy, Pappu L. N.↗

NASA NTRS1988

Finite element substructuring methods for composite mechanics

Murthy, P. L. N.↗

DOE OSTI2021

Modeling and analyzing parasitic parameters in high frequency converters

This research focuses on electromagnetic interference (EMI) / electromagnetic compatibility (EMC) design and analysis in power electronics systems. To limit the EMI under the standards, different methods and strategies are investigated. Parasitic parameters of high frequency (HF) transformer are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements for different structures and windings arrangements. Also, the magnetic field, electric field, electric displacement, and electric potential distribution are simulated and analyzed. Moreover, a high voltage system is considered and analyzed to improve the EMC. The EMI propagation paths are analyzed. The EMI noise level of the system is obtained and compared to the IEC61800-3 standard. To improve the EMC, the parasitic parameters of the transformer, as the main path of EMI circulation, are analyzed and optimized to block the propagation. Furthermore, the geometry structure of the HF transformer is optimized to lower the parasitics in the system. Three pareto-optimal techniques are investigated for the optimization. The models and results are verified by 3D-FEM and experimental results for several given scenarios. Furthermore, the EMC modeling and conducted EMI analysis are developed for a system including an AC-DC-DC power supply (rectifier and dual active bridge (DAB) converter). Moreover, the common mode (CM) EMI noise propagation through the system is discussed and the noise sources and effect of components on the noise are analyzed. Additionally, the CM impedance of different parts of the system and the noise levels are discussed. Finally, EMI attenuation techniques were applied to the system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1994

A new look at the simultaneous analysis and design of structures

The minimum weight optimization of structural systems, subject to strength and displacement constraints as well as size side constraints, was investigated by the Simultaneous ANalysis and Design (SAND) approach. As an optimizer, the code NPSOL was used which is based on a sequential quadratic programming (SQP) algorithm. The structures were modeled by the finite element method. The finite element related input to NPSOL was automatically generated from the input decks of such standard FEM/optimization codes as NASTRAN or ASTROS, with the stiffness matrices, at present, extracted from the FEM code ANALYZE. In order to avoid ill-conditioned matrices that can be encountered when the global stiffness equations are used as additional nonlinear equality constraints in the SAND approach (with the displacements as additional variables), the matrix displacement method was applied. In this approach, the element stiffness equations are used as constraints instead of the global stiffness equations, in conjunction with the nodal force equilibrium equations. This approach adds the element forces as variables to the system. Since, for complex structures and the associated large and very sparce matrices, the execution times of the optimization code became excessive due to the large number of required constraint gradient evaluations, the Kreisselmeier-Steinhauser function approach was used to decrease the computational effort by reducing the nonlinear equality constraint system to essentially a single combined constraint equation. As the linear equality and inequality constraints require much less computational effort to evaluate, they were kept in their previous form to limit the complexity of the KS function evaluation. To date, the standard three-bar, ten-bar, and 72-bar trusses have been tested. For the standard SAND approach, correct results were obtained for all three trusses although convergence became slower for the 72-bar truss. When the matrix displacement method was used, correct results were still obtained, but the execution times became excessive due to the large number of constraint gradient evaluations required. Using the KS function, the computational effort dropped, but the optimization seemed to become less robust. The investigation of this phenomenon is continuing. As an alternate approach, the code MINOS for the optimization of sparse matrices can be applied to the problem in lieu of the Kreisselmeier-Steinhauser function. This investigation is underway.

Striz, Alfred G.↗

DOE OSTI2020

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

In this study, two modifications are introduced for improving the accuracy, versatility, and robustness of a class of hybrid methods for radiation transport. In general, such methods are constructed by splitting the radiative flux into collided and uncollided components to which low- and high-resolution angular approximations are applied, respectively. In this work we focus on discrete ordinates discretizations of high and low order. The first modification we introduce changes the way in which the collided component is mapped into the uncollided component at the end of each time step in a simulation. The new mapping is a Nyström-type reconstruction that is applicable to arbitrary discrete ordinates quadratures, is guaranteed to preserve positivity of the solution provided that all ordinate weights are positive, is significantly more accurate than previous methods, and can be readily extended to other discretizations such as moment methods, finite element methods, and diffusion approximations. The second modification leverages integral deferred correction (IDC) to iteratively correct for the splitting error introduced by the inconsistency in angular discretization between the collided and uncollided components, in addition to improving the accuracy of the low-order temporal error that is treated by traditional IDC methods. Numerical tests in one- and two-dimensional geometries are used to demonstrate the increased accuracy and efficiency of the proposed modifications. It is found that the two techniques combined yield methods with solution accuracy and memory requirements comparable to that of monolithic discrete ordinates methods while reducing runtime by as much as a factor of between two and ten, depending on the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Investigation of Various Transformer Topologies for HF Isolation Applications

High-frequency (HF) transformers are an essential part of many power electronic devices. The performance and behavior of HF transformers can greatly affect the efficiency and performance of all systems, particularly, from a parasitic parameter point of view. In this article, HF transformers' parasitic parameters, such as leakage inductances and parasitic capacitances, are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements of different structures and winding arrangements. Also, the magnetic field, electric field, electric displacement field, and electric potential distribution within the transformers are simulated and analyzed. Four different HF transformers with E and U cores with different windings are designed and analyzed. Investigation outcomes help to classify structures according to the trade-off between leakage inductances and series parasitic capacitances. This information can later be used for the optimal selection and design of transformers as a function of their operating frequency for any power rating and voltage level. Moreover, 3-D FEM and experimental results validate the proposed methodology to be used for designing HF transformers in high-voltage/power applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1987

Three-dimensional finite deformation, rolling contact of a hyperelastic cylinder - Formulation of the problem and computational results

In this paper, a general class of three-dimensional rolling contact problems is analyzed by finite element methods. Finite deformations and frictional contact are considered. The results of several numerical experiments are also presented.

Bass, Jon M.↗

NASA NTRS2005

Flexible Models for Solar Sail Control

Solar sails employ a unique form of propulsion, gaining momentum from incident and reflected photons. However, the momentum transferred by an individual photon is extremely small. Consequently, a solar sail must have an extremely large surface area and also be extremely light. The flexibility of the sail then must be considered when designing or evaluating control laws. In this paper, solar sail flexibility and its influence on control effectiveness is considered using idealized two-dimensional models to represent physical phenomena rather than a specific design. Differential equations of motion are derived for a distributed parameter model of a flexible solar sail idealized as a rotating central hub with two opposing flexible booms. This idealization is appropriate for solar sail designs in which the vibrational modes of the sail and supporting booms move together allowing the sail mass to be distributed along the booms in the idealized model. A reduced analytical model of the flexible response is considered. Linear feedback torque control is applied at the central hub. Two translational disturbances and a torque disturbance also act at the central hub representing the equivalent effect of deflecting sail shape about a reference line. Transient simulations explore different control designs and their effectiveness for controlling orientation, for reducing flexible motion and for disturbance rejection. A second model also is developed as a two-dimensional "pathfinder" model to calculate the effect of solar sail shape on the resultant thrust, in-plane force and torque at the hub. The analysis is then extended to larger models using the finite element method. The finite element modeling approach is verified by comparing results from a two-dimensional finite element model with those from the analytical model. The utility of the finite element modeling approach for this application is then illustrated through examples based on a full finite element model.

Weaver Smith, Suzanne↗

NASA NTRS2001

SGBEM-FEM Alternating Method for Analyzing 3D Non-Planar Cracks and Their Growth in Structural Components

The highly accurate and efficient Symmetric Galerkin Boundary Element Method (SGBEM), a Finite Element Method (FEM)-based alternating method, is proposed for analyzing three-dimensional non-planar cracks and their growth. The cracks are modeled using the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, simulating an infinite medium. The finite element method only analyzes the stress for the uncracked body. The solution for the cracked structural component is determined by an iteration procedure. This process alternates between an FEM solution for the uncracked body and the SGBEM solution for a crack in an infinite body. Numerical analysis, and the Java code used, evaluate stress intensity factors and model fatigue crack growth. Examples of non-planar cracks in infinite media and planar cracks in finite bodies, as well as growth under fatigue, show the accuracy of the method.

Nikishkov, G. P.↗

DOE OSTI2020

A smooth contact algorithm for the combined finite discrete element method

From its inception, the combined finite discrete element method has used a distributed potential contact force algorithm to resolve interaction between finite elements. The contact interaction algorithm relies on evaluation of the contact force potential field. The problem with existing algorithms is that the potential field introduces artificial numerical non-smoothness in the contact force. This work introduces a smooth potential field based on the finite element topology, and a generalized contact interaction law is constructed on top of the smooth potential field. Further, a number of validation cases for the proposed algorithm, considering different shapes of discrete elements, are presented, and detailed aspects of the proposed contact interaction law are tested with numerical examples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method

Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in NonDestructive Testing (NDT). Here, we introduce a two-dimensional implementation of the combined finitediscrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), to explicitly simulate the crack induced nonlinear elasticity in solids with both horizontal and inclined cracks. In the FDEM model, the solid is discretized into finite elements to capture the wave propagation in the bulk material, and the finite elements along the two sides of the crack also behave as discrete elements to track the normal and tangential interactions between crack surfaces. The simulation results show that for cracked models, nonlinear elasticity is generated only when the excitation amplitude is large enough to trigger the contact between crack surfaces, and the nonlinear behavior is very sensitive to the crack surface contact. The simulations reveal the influence of normal and tangential contact on the nonlinear elasticity generation. Moreover, the results demonstrate the capabilities of FDEM for decoding the causality of nonlinear elasticity in cracked solid and its potential to assist in Non-Destructive Testing (NDT).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗