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NASA NTRS1994

An anisotropic extension of Bodner's model of viscoplasticity: Model development

An anisotropic viscoplasticity model is developed as an extension of the well known Bodner model. The extension is made by replacing the effective stress of the isotropic Bodner model by one involving invariants for transverse isotropy. The resulting model retains the simplicity of Bodner's in the ease with which the material constants are determined experimentally. It allows a representation of strong initial anisotropy yet is based on the scalar state variable under the assertion that induced anisotropy is negligible relative to the strong initial anisotropy. Temperature dependence is taken as in the original Bodner theory. Account is made of fiber volume fraction through nonlinear rules of mixture applied to the stress history and anisotropy parameters. Focus is on the theoretical development of the model, however, application to a W/Cu composite is in progress and will be reported as a sequel to this report.

Robinson, David N.↗

NASA NTRS1994

Coupled electromechanical response of composite beams with embedded piezoelectric sensors and actuators

Unified mechanics are developed with the capability to model both sensory and active composite laminates with embedded piezoelectric layers. A discrete-layer formulation enables analysis of both global and local electromechanical response. The mechanics include the contributions from elastic, piezoelectric, and dielectric components. The incorporation of electric potential into the state variables permits representation of general electromechanical boundary conditions. Approximate finite element solutions for the static and free-vibration analysis of beams are presented. Applications on composite beams demonstrate the capability to represent either sensory or active structures and to model the complicated stress-strain fields, the interactions between passive/active layers, interfacial phenomena between sensors and composite plies, and critical damage modes in the material. The capability to predict the dynamic characteristics under various electrical boundary conditions is also demonstrated.

Saravanos, D. A.↗

NASA NTRS1994

A Fully Associative, Non-Linear Kinematic, Unified Viscoplastic Model for Titanium Based Matrices

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential based multiaxial unified viscoplastic model is obtained. This model possesses one tensorial internal state variable that is associated with dislocation substructure, with an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of non-linear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This non-linear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated) and greatly influences the multiaxial response under non-proportional loading paths. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. Specification of an experimental program for the complete determination of the material functions and parameters for characterizing a metallic matrix, e.g., TIMETAL 21S, is given. The experiments utilized are tensile, creep, and step creep tests. Finally, a comparison of this model and a commonly used Bodner-Partom model is made on the basis of predictive accuracy and numerical efficiency.

Arnold, S. M.↗

NASA NTRS1991

Alleviation of whirl-flutter on a joined-wing tilt-rotor aircraft configuration using active controls

The feasibility of using active controls to delay the onset of whirl-flutter on a joined-wing tilt rotor aircraft was investigated. The CAMRAD/JA code was used to obtain a set of linear differential equations which describe the motion of the joined-wing tilt-rotor aircraft. The hub motions due to wing/body motion is a standard input to CAMRAD/JA and were obtained from a structural dynamics model of a representative joined-wing tilt-rotor aircraft. The CAMRAD/JA output, consisting of the open-loop system matrices, and the airframe free vibration motion were input to a separate program which performed the closed-loop, active control calculations. An eigenvalue analysis was performed to determine the flutter stability of both open- and closed-loop systems. Sensor models, based upon the feedback of pure state variables and based upon hub-mounted sensors, providing physically measurable accelerations, were evaluated. It was shown that the onset of tilt-rotor whirl-flutter could be delayed from 240 to above 270 knots by feeding back vertical and span-wise accelerations, measured at the rotor hub, to the longitudinal cyclic pitch. Time response calculations at a 270-knot cruise condition showed an active cyclic pitch control level of 0.009 deg, which equates to a very acceptable 9 pound active-control force applied at the rotor hub.

Vanaken, Johannes M.↗

NASA NTRS1994

Micromechanical modeling of damage growth in titanium based metal-matrix composites

The thermomechanical behavior of continuous-fiber reinforced titanium based metal-matrix composites (MMC) is studied using the finite element method. A thermoviscoplastic unified state variable constitutive theory is employed to capture inelastic and strain-rate sensitive behavior in the Timetal-21s matrix. The SCS-6 fibers are modeled as thermoplastic. The effects of residual stresses generated during the consolidation process on the tensile response of the composites are investigated. Unidirectional and cross-ply geometries are considered. Differences between the tensile responses in composites with perfectly bonded and completely debonded fiber/matrix interfaces are discussed. Model simulations for the completely debonded-interface condition are shown to correlate well with experimental results.

Sherwood, James A.↗

NASA NTRS1994

Vibration suppression with approximate finite dimensional compensators for distributed systems: Computational methods and experimental results

Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.

Banks, H. T.↗

NASA NTRS1994

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Heyliger, P. R.↗

NASA NTRS1993

Ducted fan acoustic radiation including the effects of nonuniform mean flow and acoustic treatment

Forward and aft acoustic propagation and radiation from a ducted fan is modeled using a finite element discretization of the acoustic field equations. The fan noise source is introduced as equivalent body forces representing distributed blade loading. The flow in and around the nacelle is assumed to be nonuniform, reflecting the effects of forward flight and flow into the inlet. Refraction due to the fan exit jet shear layer is not represented. Acoustic treatment on the inlet and exhaust duct surfaces provides a mechanism for attenuation. In a region enclosing the fan a pressure formulation is used with the assumption of locally uniform flow. Away from the fan a velocity potential formulation is used and the flow is assumed nonuniform but irrotational. A procedure is developed for matching the two regions by making use of local duct modal amplitudes as transition state variables and determining the amplitudes by enforcing natural boundary conditions at the interface between adjacent regions in which pressure and velocity potential are used. Simple models of rotor alone and rotor/exit guide vane generated noise are used to demonstrate the calculation of the radiated acoustic field and to show the effect of acoustic treatment. The model has been used to assess the success of four techniques for acoustic lining optimization in reducing far field noise.

Eversman, Walter↗

NASA NTRS1992

Cognition and procedure representational requirements for predictive human performance models

Models and modeling environments for human performance are becoming significant contributors to early system design and analysis procedures. Issues of levels of automation, physical environment, informational environment, and manning requirements are being addressed by such man/machine analysis systems. The research reported here investigates the close interaction between models of human cognition and models that described procedural performance. We describe a methodology for the decomposition of aircrew procedures that supports interaction with models of cognition on the basis of procedures observed; that serves to identify cockpit/avionics information sources and crew information requirements; and that provides the structure to support methods for function allocation among crew and aiding systems. Our approach is to develop an object-oriented, modular, executable software representation of the aircrew, the aircraft, and the procedures necessary to satisfy flight-phase goals. We then encode in a time-based language, taxonomies of the conceptual, relational, and procedural constraints among the cockpit avionics and control system and the aircrew. We have designed and implemented a goals/procedures hierarchic representation sufficient to describe procedural flow in the cockpit. We then execute the procedural representation in simulation software and calculate the values of the flight instruments, aircraft state variables and crew resources using the constraints available from the relationship taxonomies. The system provides a flexible, extensible, manipulative and executable representation of aircrew and procedures that is generally applicable to crew/procedure task-analysis. The representation supports developed methods of intent inference, and is extensible to include issues of information requirements and functional allocation. We are attempting to link the procedural representation to models of cognitive functions to establish several intent inference methods including procedural backtracking with concurrent search, temporal reasoning, and constraint checking for partial ordering of procedures. Finally, the representation is being linked to models of human decision making processes that include heuristic, propositional and prescriptive judgement models that are sensitive to the procedural content in which the valuative functions are being performed.

Corker, K.↗

NASA NTRS1994

Experimental verification of a progressive damage model for composite laminates based on continuum damage mechanics

Progressive failure is a crucial concern when using laminated composites in structural design. Therefore the ability to model damage and predict the life of laminated composites is vital. The purpose of this research was to experimentally verify the application of the continuum damage model, a progressive failure theory utilizing continuum damage mechanics, to a toughened material system. Damage due to tension-tension fatigue was documented for the IM7/5260 composite laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables, respectively, to predict stiffness loss. A damage dependent finite element code qualitatively predicted trends in transverse matrix cracking, axial splits and local stress-strain distributions for notched quasi-isotropic laminates. The predictions were similar to the experimental data and it was concluded that the continuum damage model provided a good prediction of stiffness loss while qualitatively predicting damage growth in notched laminates.

Coats, Timothy William↗

NASA NTRS1995

Shapes and stability of algebraic nuclear models

A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

Lopez-Moreno, Enrique↗

NASA NTRS1995

Damage-mitigating control of a reusable rocket engine for high performance and extended life

The goal of damage mitigating control in reusable rocket engines is to achieve high performance with increased durability of mechanical structures such that functional lives of the critical components are increased. The major benefit is an increase in structural durability with no significant loss of performance. This report investigates the feasibility of damage mitigating control of reusable rocket engines. Phenomenological models of creep and thermo-mechanical fatigue damage have been formulated in the state-variable setting such that these models can be combined with the plant model of a reusable rocket engine, such as the Space Shuttle Main Engine (SSME), for synthesizing an optimal control policy. Specifically, a creep damage model of the main thrust chamber wall is analytically derived based on the theories of sandwich beam and viscoplasticity. This model characterizes progressive bulging-out and incremental thinning of the coolant channel ligament leading to its eventual failure by tensile rupture. The objective is to generate a closed form solution of the wall thin-out phenomenon in real time where the ligament geometry is continuously updated to account for the resulting deformation. The results are in agreement with those obtained from the finite element analyses and experimental observation for both Oxygen Free High Conductivity (OFHC) copper and a copper-zerconium-silver alloy called NARloy-Z. Due to its computational efficiency, this damage model is suitable for on-line applications of life prediction and damage mitigating control, and also permits parametric studies for off-line synthesis of damage mitigating control systems. The results are presented to demonstrate the potential of life extension of reusable rocket engines via damage mitigating control. The control system has also been simulated on a testbed to observe how the damage at different critical points can be traded off without any significant loss of engine performance. The research work reported here is built upon concepts derived from the disciplines of Controls, Thermo-fluids, Structures, and Materials. The concept of damage mitigation, as presented in this report, is not restricted to control of rocket engines. It can be applied to any system where structural durability is an important issue.

Ray, Asok↗

NASA NTRS1995

A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium alloys

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential base multiaxial, nonisothermal unified viscoplastic model is obtained. This model possesses one tensorial internal state variable (that is, associated with dislocation substructure) and an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated), greatly influences the multiaxial response under non-proportional loading paths, and in the case of nonisothermal histories, introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. The specific model proposed is characterized for a representative titanium alloy commonly used as the matrix material in SiC fiber reinforced composites, i.e., TIMETAL 21S. Verification of the proposed model is shown using 'specialized' non-standard isothermal and thermomechanical deformation tests.

Arnold, S. M.↗

NASA NTRS1995

Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations.

Markopoulos, Nikos↗

NASA NTRS1995

Tracking magnetogram proper motions by multiscale regularization

Long uninterrupted sequences of solar magnetograms from the global oscillations network group (GONG) network and from the solar and heliospheric observatory (SOHO) satellite will provide the opportunity to study the proper motions of magnetic features. The possible use of multiscale regularization, a scale-recursive estimation technique which begins with a prior model of how state variables and their statistical properties propagate over scale. Short magnetogram sequences are analyzed with the multiscale regularization algorithm as applied to optical flow. This algorithm is found to be efficient, provides results for all the spatial scales spanned by the data and provides error estimates for the solutions. It is found that the algorithm is less sensitive to evolutionary changes than correlation tracking.

Jones, Harrison P.↗

NASA NTRS1996

Analysis of Sensory/Active Piezoelectric Composite Structures in Thermal Environments

Although there has been extensive development of analytical methods for modeling the behavior of piezoelectric structures, only a limited amount of research has been performed concerning the implications of thermal effects on both the active and sensory response of smart structures. Thermal effects become important when the piezoelectric structure has to operate in either extremely hot or cold temperature environments. Consequently, the purpose of this paper is to extend the previously developed discrete layer formulation of Saravanos and Heyliger to account for the coupled mechanical, electrical, and thermal response in modern smart composite beams. The mechanics accounts for thermal effects which may arise in the elastic and piezoelectric media at the material level through the constitutive equations. The displacements, electric potentials, and temperatures are introduced as state variables, allowing them to be modeled as variable fields through the laminate thickness. This unified representation leads to an inherent capability to model both the active compensation of thermal distortions in smart structures and the resultant sensory voltage when thermal loads are applied. The corresponding finite element formulation is developed and numerical results demonstrate the ability to model both the active and sensory modes of composite beams with heterogeneous plies with attached piezoelectric layers under thermal loadings.

Lee, Ho-Jun↗

NASA NTRS1996

H Infinity Control of Magnetic Bearings to Ensure Both System and External Periodic Disturbance Robustness

Both self-excited and forced disturbances often lead to severe rotor vibrations in a magnetic bearing systems with long slender shafts. This problem has been studied using the H-infinity method, and stability with good robustness can be achieved for the linearized model of a magnetic bearing when small transient disturbances are applied. In this paper, the H-infinity control method for self-excited and forced disturbances is first reviewed. It is then applied to the control of a magnetic bearing rotor system. In modelling the system, the shaft is first discretized into 18 finite elements and then three levels of condensation are applied. This leads to a system with three masses and three compliant elements which can be described by six state variable coordinates. Simulation of the resultant system design has been performed at speeds up to 10,000 rpm. Disturbances in terms of different initial displacements, initial impulses, and external periodic inputs have been imposed. The simulation results show that good stability can be achieved under these different transient disturbances using the proposed controller while at the same time reducing the sensitivity to external periodic disturbances.

Jiang, Yuhong↗

NASA NTRS1995

Experimental Verification of a Progressive Damage Model for IM7/5260 Laminates Subjected to Tension-Tension Fatigue

The durability and damage tolerance of laminated composites are critical design considerations for airframe composite structures. Therefore, the ability to model damage initiation and growth and predict the life of laminated composites is necessary to achieve structurally efficient and economical designs. The purpose of this research is to experimentally verify the application of a continuum damage model to predict progressive damage development in a toughened material system. Damage due to monotonic and tension-tension fatigue was documented for IM7/5260 graphite/bismaleimide laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables to predict stiffness loss in unnotched laminates. A damage dependent finite element code predicted the stiffness loss for notched laminates with good agreement to experimental data. It was concluded that the continuum damage model can adequately predict matrix damage progression in notched and unnotched laminates as a function of loading history and laminate stacking sequence.

Coats, Timothy W.↗