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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Line spring model and its applications to part-through crack problems in plates and shells

The line spring model is described and extended to cover the problem of interaction of multiple internal and surface cracks in plates and shells. The shape functions for various related crack geometries obtained from the plane strain solution and the results of some multiple crack problems are presented. The problems considered include coplanar surface cracks on the same or opposite sides of a plate, nonsymmetrically located coplanar internal elliptic cracks, and in a very limited way the surface and corner cracks in a plate of finite width and a surface crack in a cylindrical shell with fixed end.

Erdogan, Fazil↗
NASA NTRS1989

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity-pressure integrated method, yields accurate computational results for high-Reynolds-number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity-pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow of Reynolds number 10000, a laminar backward-facing step flow and a laminar flow through a nest of cylinders.

Kim, S.-W.↗
NASA NTRS1989

Line mixing effects in solar occultation spectra of the lower stratosphere - Measurements and comparisons with calculations for the 1932/cm CO2 Q branch

Line mixing effects have been observed in a CO2 Q branch recorded in 0.01/cm-resolution IR solar occultation spectra of the lower stratosphere. The spectral data were obtained by the Atmospheric Trace Molecule Spectroscopy Fourier transform spectrometer during the Spacelab 3 mission in the spring of 1985. Analysis of the 1932.47/cm Q branch of (C-12)(O-16)2 shows absorption coefficients below the band origin about 0.62 times those calculated using a standard Voigt line-shape function. Calculations of line mixing using the Lorentz halfwidths of the lines and a simple energy-gap scaling law to parameterize rotational energy transfer reproduce the observed absorption coefficients to about 10 percent. The present results provide the first quantitative information on air-broadened line mixing effects in a Q branch at low temperatures (about 210 K) and show that these effects are significant even at the low pressures of the lower stratosphere (about 100 mbar).

Rinsland, Curtis P.↗
NASA NTRS1989

A partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computer

A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.

Noor, Ahmed K.↗
NASA NTRS1989

A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

Hodges, Dewey H.↗
NASA NTRS1989

A finite element approach for large motion dynamic analysis of multibody structures in space

A three-dimensional finite element formulation for modeling the transient dynamics of constrained multibody space sructures with truss-like configurations is presented. Convected coordinate systems are used to define rigid-body motion of individual elements in the system. These systems are located at one end of each element and are oriented such that one axis passes through the other end of the element. Deformation of each element, relative to its convected coordinate system, is defined by cubic flexural shape functions as used in finite element methods of structural analysis. The formulation is oriented toward joint dominated structures and places the generalized coordinates at the joint. A transformation matrix is derived to integrate joint degree-of-freedom into the equations of motion of the element. Based on the derivation, a general-purpose code LATDYN (Large Angle Transient DYNamics) was developed. Two examples are presented to illustrate the application of the code. For the spin-up of a flexible beam, results are compared with existing solutions available in the literature. For the deployment of one bay of a deployable space truss (the Minimast), results are verified by the geometric knowledge of the system and converged solution of a successively refined model.

Chang, Che-Wei↗
NASA NTRS1989

The dynamics and control of large flexible space structures - 12, supplement 11

The rapid 2-D slewing and vibrational control of the unsymmetrical flexible SCOLE (Spacecraft Control Laboratory Experiment) with multi-bounded controls is considered. Pontryagin's Maximum Principle is applied to the nonlinear equations of the system to derive the necessary conditions for the optimal control. The resulting two point boundary value problem is then solved by using the quasilinearization technique, and the near minimum time is obtained by sequentially shortening the slewing time until the controls are near the bang-bang type. The tradeoff between the minimum time and the minimum flexible amplitude requirements is discussed. The numerical results show that the responses of the nonlinear system are significantly different from those of the linearized system for rapid slewing. The SCOLE station-keeping closed loop dynamics are re-examined by employing a slightly different method for developing the equations of motion in which higher order terms in the expressions for the mast modal shape functions are now included. A preliminary study on the effect of actuator mass on the closed loop dynamics of large space systems is conducted. A numerical example based on a coupled two-mass two-spring system illustrates the effect of changes caused in the mass and stiffness matrices on the closed loop system eigenvalues. In certain cases the need for redesigning control laws previously synthesized, but not accounting for actuator masses, is indicated.

Bainum, Peter M.↗
NASA NTRS1989

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗
NASA NTRS1990

Nonlinear analysis of compressively loaded linked-plate structures

A method is presented for the geometrically nonlinear analysis of the equilibrium behavior of a general class of compressively loaded, prismatic, linked-plate structures. The semi-analytical method accounts for geometric shape imperfections, and allows the use of laminated composite plate properties. Buckling eigenfunctions are used as displacement shape functions, and the associated second-order displacement fields are incorporated. The nonlinear plate equilibrium equations are expressed in terms of the assumed displacement form, and the Galerkin method is used to obtain a set of algebraic equations which are nonlinear in the modal amplitudes and the load parameter. Buckling eigensolutions for the class of structures under consideration can be obtained from the VIPASA computer code; thus, subject to some additional restrictions in loading and plate anisotropy, structural configurations which can be analyzed with regard to buckling response by VIPASA can be analyzed with regard to geometrically nonlinear response using the new method.

Stoll, Frederick↗
NASA NTRS1989

Advanced applications of BEM to inelastic analysis of solids

Newly evolved boundary element solution algorithms are utilized for solving a range of elastoplastic and thermoplastic problems. The first algorithm is the typical iterative procedure in which the unknown boundary solution and the initial stress (or strain) rates are found together in an incremental iterative fashion. The second one is a variable stiffness type approach in which the incremental boundary solution is obtained in a direct (noniterative) manner. The third procedure differs from the two prior algorithms in that volume integration is not needed to incorporate the nonlinear effects in the analysis. Instead, initial stress rates are introduced in the boundary element system by way of particular integrals. The methodology is used in a general purpose, multiregion system that employs quadratic isoparametric shape functions to model the geometry and field variables of the body and can admit up to 15 substructured areas of different material properties.

Banerjee, P. K.↗
NASA NTRS1990

Combined design of structures and controllers for optimal maneuverability

Approaches to the combined design of structures and controllers for achieving optimal maneuverability are presented. A maneuverability index which directly reflects the minimum time required to perform a given set of maneuvers is introduced. By designing the flexible appendages, the maneuver time of the spacecraft is minimized under the constraints of structural properties, and post maneuver spillover is kept within a specified bound. The spillover reduction is achieved by making use of an appropriate reduced order model. The distributed parameter design problem is approached using assumed shape functions, and finite element analysis with dynamic reduction. Solution procedures have been investigated. Approximate design methods have been developed to overcome the computational difficulties. Some new constraints on the modal frequencies of the spacecraft are introduced in the original optimization problem to facilitate the solution process. It is shown that the global optimal design may be obtained by tuning the natural frequencies to satisfy specific constraints. Researchers quantify the difference between a lower bound to the solution for maneuver time associated with the original problem and the estimate obtained from the modified problem, for a specified application requirement. Numerical examples are presented to demonstrate the capability of this approach.

Ling, Jer↗
NASA NTRS1990

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗
NASA NTRS1990

Development of BEM for ceramic composites

Details on the progress made during the first three years of a five-year program towards the development of a boundary element code are presented. This code was designed for the micromechanical studies of advance ceramic composites. Additional effort was made in generalizing the implementation to allow the program to be applicable to real problems in the aerospace industry. The ceramic composite formulations developed were implemented in the three-dimensional boundary element computer code BEST3D. BEST3D was adopted as the base for the ceramic composite program, so that many of the enhanced features of this general purpose boundary element code could by utilized. Some of these facilities include sophisticated numerical integration, the capability of local definition of boundary conditions, and the use of quadratic shape functions for modeling geometry and field variables on the boundary. The multi-region implementation permits a body to be modeled in substructural parts; thus dramatically reducing the cost of the analysis. Furthermore, it allows a body consisting of regions of different ceramic matrices and inserts to be studied.

Henry, D. P.↗
NASA NTRS1990

Effect of shaping sensor data on pilot response

The pilot of a modern jet aircraft is subjected to varying workloads while being responsible for multiple, ongoing tasks. The ability to associate the pilot's responses with the task/situation, by modifying the way information is presented relative to the task, could provide a means of reducing workload. To examine the feasibility of this concept, a real time simulation study was undertaken to determine whether preprocessing of sensor data would affect pilot response. Results indicated that preprocessing could be an effective way to tailor the pilot's response to displayed data. The effects of three transformations or shaping functions were evaluated with respect to the pilot's ability to predict and detect out-of-tolerance conditions while monitoring an electronic engine display. Two nonlinear transformations, on being the inverse of the other, were compared to a linear transformation. Results indicate that a nonlinear transformation that increases the rate-or-change of output relative to input tends to advance the prediction response and improve the detection response, while a nonlinear transformation that decreases the rate-of-change of output relative to input tends to lengthen the prediction response and make detection more difficult.

Bailey, Roger M.↗
NASA NTRS1990

Development of an integrated BEM approach for hot fluid structure interaction

A comprehensive boundary element method is presented for transient thermoelastic analysis of hot section Earth-to-Orbit engine components. This time-domain formulation requires discretization of only the surface of the component, and thus provides an attractive alternative to finite element analysis for this class of problems. In addition, steep thermal gradients, which often occur near the surface, can be captured more readily since with a boundary element approach there are no shape functions to constrain the solution in the direction normal to the surface. For example, the circular disc analysis indicates the high level of accuracy that can be obtained. In fact, on the basis of reduced modeling effort and improved accuracy, it appears that the present boundary element method should be the preferred approach for general problems of transient thermoelasticity.

Dargush, G. F.↗
NASA NTRS1991

Time-domain finite elements in optimal control with application to launch-vehicle guidance

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

Bless, Robert R.↗
NASA NTRS1990

On the partitioning strategy based on symmetry transformations

A computational procedure is presented for the analysis of unsymmetric structures. The procedure is based on a modified version of the symmetry-transformation partitioning strategy, in which the response of the structure is approximated by a linear combination of symmetric/antisymmetric response vectors, each obtained by using only a fraction of the degrees of freedom of the original FEM model. The three key elements of the procedure are: (1) mixed (or primitive-variable) formulation with independent shape functions for the different fields; (2) restructuring of the governing discrete equations of the structure into uncoupled sets in the symmetric and antisymmetric response vectors; and (3) a stable and efficient iterative process for generating the response of the structure. The effectiveness of the proposed procedure and its advantages over classical substructuring are demonstrated by means of numerical examples.

Noor, Ahmed K.↗
NASA NTRS1991

Weak Hamiltonian finite element method for optimal control problems

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.↗