Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stiff problem”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Radiative interactions in chemically reacting supersonic internal flows

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation for hydrogen-air systems. The chemistry source terms in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a ten-degree compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assure nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species and that this can have a significant influence on the flowfield.

Tiwari, S. N.↗
NASA NTRS1991

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Haftka, Raphael T.↗
NASA NTRS1991

Radiative interactions in a hydrogen-fueled supersonic combustor

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation, for hydrogen-air systems. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a 10-deg compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assume nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudogray model is used to represent the absorption-emission characteristics of the participating species. Results otained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species, and that this can have a significant influence on the flowfield.

Chandrasekhar, R.↗
NASA NTRS1992

Thermochemical nonequilibrium and radiative interactions in supersonic hydrogen-air combustion

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with nonequilibrium chemistry and thermodynamics, coupled with radiation, for hydrogen-air systems. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed, expanding flow in a supersonic nozzle. The reacting flow consists of seven species, one of which is the inert N2 molecule. The thermal state of the gas is modeled with one translational-rotational temperature and five vibrational temperatures. The harmonic oscillator model is used in the formulation for vibrational relaxation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate the presence of nonequilibrium in the expansion region. This reduces the radiative interactions and can have a significant influence on the flowfield.

Chandrasekhar, R.↗
NASA NTRS1991

High temperature structural fibers: Status and needs

The key to high temperature structural composites is the selection and incorporation of continuous fiber reinforcement with optimum mechanical, physical, and chemical properties. Critical fiber property needs are high strength, high stiffness, and retention of these properties during composite fabrication and use. However, unlike polymeric composites where all three requirements are easily achieved with a variety of commercially available carbon-based fibers, structural fibers with sufficient stiffness and strength retention for high temperature metal, intermetallic, and ceramic composites are not available. The objective here is to discuss in a general manner the thermomechanical stability problem for current high performance fibers which are based on silicon and alumina compositions. This is accomplished by presenting relevant fiber property data with a brief discussion of potential underlying mechanisms. From this general overview, some possible materials engineering approaches are suggested which may lead to minimization and/or elimination of this critical stability problem for current high temperature fibers.

Dicarlo, James A.↗
NASA NTRS1990

Finite element analysis and optimization of composite structures

Linearly elastic fiber reinforced composite discs and laminates in plane stress with variable local orientation and concentration of one or two fiber fields embedded in the matrix material, are considered. The thicknesses and the domain of the discs or laminates are assumed to be given, together with prescribed boundary conditions and in-plane loading along the edge. The problem under study consists in determining throughout the structural domain the optimum orientations and concentrations of the fiber fields in such a way as to maximize the integral stiffness of the composite disc or laminate under the seven loading. Minimization of the integral stiffness can also be performed. The optimization is performed subject to a prescribed bound on the total cost or weight of the composite that for given unit cost factors or specific weights determines the amounts of fiber and matrix materials in the structure. Examples are presented.

Thomsen, Jan↗
NASA NTRS2021

Modeling and Analysis of Fluted-Core Composite Structures for Aerospace Applications

Fiber-reinforced composites are becoming more frequently used for aerospace applications, and because of mass and stiffness requirements, sandwich composites are often selected where shell-type structures are needed. However, traditional-core sandwich composites can exhibit certain manufacturing and in-service problems that have the potential to be alleviated through the use of other sandwich composite concepts. Fluted-core sandwich composite structures, which consist of integral angled web members with structural radius fillers, or noodles, spaced between laminate face sheets, is one such alternative and is considered herein. Because the noodles can consist of unidirectional fiber and can represent a significant amount of the total fluted-core cross section, accurate prediction of the structural response requires that the noodles be modeled with sufficient detail. Previous work showed that the structural response of fluted-core sandwich composite structures could be accurately represented with detailed finite element analysis using a combination of solid and shell elements. In these models, solid elements were used to represent the noodles and shell elements were used to represent the webs and faces. However, this previous solid-noodle modeling approach was also quite computationally intensive, and therefore not practical for large or complicated structures. In this document, a less computationally intensive shell-noodle approach, wherein the entire fluted-core sandwich composite construction is modeled with shell elements, is discussed and predicted structural responses are compared with those of the solid-noodle approach. It is found that by proper selection of certain geometric parameters (thickness and offset of the shell elements that represent the noodle), the shell-noodle modeling approach can be made “structurally equivalent” to the solid-noodle modelling approach.

Leonard Oremont↗
NASA NTRS2019

Modeling and simulation challenges for softgoods in space deployable structures

This paper examines modeling and simulation challenges for deployable spacecraft structures with softgood components. Previous studies highlighted the numerical challenges due to the mixture of high stiffness and low stiffness contact in this class of structures. This paper examines the use of the commercial LS-DYNA nonlinear finite element code on a set of relevant benchmark problems.

Mobrem, Mehran↗
NASA NTRS2006

Multimodal Platform Control for Robotic Planetary Exploration Missions

Planetary exploration missions pose unique problems for astronauts seeking to coordinate and control exploration vehicles. These include working in an environment filled with abrasive dust (e.g., regolith compositions), a desire to have effective hands-free communication, and a desire to have effective analog control of robotic platforms or end effectors. Requirements to operate in pressurized suits are particularly problematic due to the increased bulk and stiffness of gloves. As a result, researchers are considering alternative methods to perform fine movement control, for example capitalizing on higher-order voice actuation commands to perform control tasks. This paper presents current research at NASA s Neuro Engineering Laboratory that explores one method-direct bioelectric interpretation-for handling some of these problems. In this type of control system, electromyographic (EMG) signals are used both to facilitate understanding of acoustic speech in pressure-regulated suits 2nd to provide smooth analog control of a robotic platform, all without requiring fine-gained hand movement. This is accomplished through the use of non-invasive silver silver-chloride electrodes located on the forearm, throat, and lower chin, positioned so as to receive electrical activity originating from the muscles during contraction. For direct analog platform control, a small Personal Exploration Rover (PER) built by Carnegie Mellon University Robotics is controlled using forearm contraction duration and magnitudes, measured using several EMG channels. Signal processing is used to translate these signals into directional platform rotation rates and translational velocities. higher order commands were generated by differential contraction patterns called "clench codes."

Jorgensen, Charles↗
NASA NTRS1984

A simple rectangular element for 2-dimensional analysis of laminated composites

A simple rectangular finite element was developed for two dimensional analysis of laminated composite materials. The rectangular laminated composite element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffness and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed.

Whitcomb, J. D.↗
NASA NTRS1986

A simple nonlinear joint model

Hertzian contact theory is applied to a butt joint with specially mismatched bearing surfaces to devise a simple mathematical model of nonlinear axial force-displacement behavior in jointed members. Normalized tangent stiffness-force plots, for several values of a joint imperfection parameter, are presented for the sample case of solid structural members of circular section. The results illustrate the potential problem of high joint compliance at low axial-force levels, as well as the generally desirable stiffening and linearizing effects of preload. A nonlinear oscillator problem based on the static model is also formulated and solved to illustrate the effect of amplitude on natural frequency. As expected, natural frequency is low when amplitude is small. The results call attention to the important roles that tight tolerances and preload are expected to play in the design and fabrication of deployable and erectable truss-type space structures.

Fichter, W. B.↗
NASA NTRS1986

A simple rectangular element for two-dimensional analysis of laminated composites

A simple rectangular finite element was developed for two-dimensional analysis of laminated composite materials. The rectangular laminated composite element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffness and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed.

Whitcomb, J. D.↗
NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗
NASA NTRS1988

Evaluation of a methodology for model identification in the time domain

A model identification methodology for structural dynamics has been applied to simulated vibrational data as a first step in evaluating its accuracy. The evaluation has taken into account a wide variety of factors which affect the accuracy of the procedure. The effects of each of these factors were observed in both the response time histories and the estimates of the parameters of the model by comparing them with the exact values of the system. Each factor was varied independently but combinations of these have also been considered in an effort to simulate real situations. The results of the tests have shown that for the chain model, the procedure yields robust estimates of the stiffness parameters under the conditions studied whenever uniqueness is ensured. When inaccuracies occur in the results, they are intimately related to non-uniqueness conditions inherent in the inverse problem and not to shortcomings in the methodology.

Beck, R. T.↗
NASA NTRS2005

Application of Ultrasonic Guided Waves for Evaluating Aging Wire Insulation

Aging wiring has become a critical issue to the aerospace and aircraft industries due to Shuttle and aircraft incidents. The problem is that over time the insulation on wire becomes brittle and cracks. This exposes the underlying conductive wire to the potential for short circuits and fire. Popular methods of monitoring aging wire problems focuses on applying electrical sensing techniques that are sensitive to the conductor's condition, but not very sensitive to the wire insulation's condition. Measurement of wire insulation stiffness and ultrasonic properties by ultrasonic guided waves is being examined. Experimental measurements showed that the lowest order extensional mode could be sensitive to stiffness changes in the wire insulation. To test this theory conventional wire samples were heat damaged in an oven, in a range of heating conditions. The samples were 12, 16, and 20 gauge and the heat damage introduced material changes in the wire insulation that made the originally flexible insulation brittle and darker in color. Results showed that extensional mode phase velocity increased for the samples that were exposed to heat for longer duration.

Anastasi, Robert F.↗
NASA NTRS1975

Numerical solution of quadratic matrix equations for free vibration analysis of structures

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

Gupta, K. K.↗
NASA NTRS1978

Dynamic model verification of large structural systems

The objective of the present methodology is two-fold: (1) to process test data obtained from either modal survey tests, or slow sine-sweep tests, to extract a set of orthogonal modes best matching the test data while being commensurate with the dynamic model, and (2) to modify submatrices of the dynamic model mass and stiffness matrices to adjust the model to best fit the test data. The method has been implemented using a linear statistical sequential estimator for computation on a CDC computer. Demonstration problems involving Space Shuttle quarter-scale vibration test data and dynamic models have been run. This paper will discuss the general methodology and experience to date.

Lee, L. T.↗
NASA NTRS1981

Development of an orthotropic hole element

A finite element was developed which adequately represents the state of stress in the region around a circular hole in orthotropic material experiencing reasonably general loading. This was achieved with a complementary virtual work formulation of the stiffness and stress matrices for a square element with center circular hole. The assumed stress state provides zero shearing stress on the hole boundary, so the element is suitable for problems involving load transfer without friction. The element has been implemented in the NASTRAN computer program, and sample problem results are presented.

Smith, C. V.↗