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NASA NTRS1978

Elastic constants at low temperatures - Recent measurements on technological materials at NBS

Solid-state low-temperature elastic properties have been experimentally studied at the NBS Cryogenic Division for four years. Most studies were between room temperature and liquid-helium temperature; some were only to liquid-nitrogen temperature. Two dynamic (high-frequency) experimental methods were used, pulse-echo and resonance, resulting in adiabatic elastic constants. The present paper reviews these studies for 47 technological materials - metals, alloys, and composites. The elastic constants primarily discussed are Young's modulus, the shear modulus, the bulk modulus (reciprocal compressibility), and Poisson's ratio. A summary table is presented to show which base metals tend to exhibit regular, irregular, or anomalous behavior in their elastic constant/temperature curves.

Ledbetter, H. M.↗

NASA NTRS1980

Post-buckling behavior of a beam-column on a nonlinear elastic foundation with a gap

The structural behavior of an elastic beam-column placed with a gap between two nonlinearity elastic layers each resting on a rigid foundation was examined. The beam-column was laterally supported at both ends and subjected to a uniform transverse load and axial compression. Its slenderness was such that the axial compressive force exceeds the amount that would be necessary to buckle it as a simple supported column. The elastic layers were represented by an elastic foundation with a strongly nonlinear specific reaction taken as a rapidly increasing function of the layer compression. The analytical model developed simulated the entire pattern of the deflection and stress state including layer and end support reactions, under gradually increasing axial force.

Kuznetsov, E. N.↗

NASA NTRS1980

Elastic scattering and vibrational excitation of CO2 by 4, 10, 20 and 50 eV electrons

Elastic and vibrationally inelastic differential, integral and momentum-transfer cross sections for electrons scattered by CO2 molecules are reported at 4, 10, 20 and 50 eV impact energies. The elastic cross sections are placed on an absolute scale by means of a relative flow technique. The inelastic cross sections are normalised to the elastic ones by using the inelastic to elastic intensity ratios. Data are reported for up to ten features in the 0.0 to 0.4 eV energy-loss region.

NASA NTRS1981

An analytical pilot rating method for highly elastic aircraft

An analytical method was developed to predict pilot ratings for highly elastic aircraft subject to severe mode interactions between rigid body and elastic dynamics. An extension of the standard optimal control model of pilot response was made to include the hypothesis that the pilot controls the system with an internal model consisting of the slowly varying part of the aircraft dynamics. This modified optimal control model was analytically evaluated for a longitudinal pitch tracking task on a large flexible aircraft. Parametric variations in the undamped natural frequencies of two symmetric elastic modes were made to induce varying amounts of mode interaction. The model proved successful in discriminating when the pilot can or cannot visually separate rigid from elastic pitch response in the turbulence excited tracking task. This method shows considerable promise in making it possible to investigate such mode interaction effects on handling qualities in the preliminary design stage of new aircraft.

Swaim, R. L.↗

NASA NTRS1983

Dynamics of Tisserand's frame for an elastic spacecraft with stored angular momentum

Tisserand's frame represents a frame in which the deformations in elastic members and the motions in a central rigid body add zero translational and angular momenta to the overall momentum of the vehicle. The considered relations have been known for some time in the case of nongyroscopic spacecraft. The present investigation is concerned with an extension of the relations to gyroscopic systems, taking into account an entirely elastic spacecraft with significant stored angular momentum. A two-dimensional free, rectangular, elastic structure with axisymmetric rotors is considered. Equations of motion are obtained with the aid of the Newton-Eulerian technique and Hamilton's principle. An analysis is conducted of the dynamics of an elastic gyroscopic free vehicle, and the dynamics of the Tisserand's frame in response to external stimuli is examined.

Hablani, H. B.↗

NASA NTRS1985

An Elastic Analysis of a Plated Bone to Determine Fracture Gap Motion

An elastic analysis to determine fracture gap motions occurring in the osteotomized and plated canine femur was performed using the finite element program NASTRAN. The femur was idealized as a hollow right cylinder, and transverse anisotropy was assumed for the elastic properties of the bone. A 3-D 360 degree model consisting of 224 isoparametric quadrilateral hexahedral and 11 beam elements was created. A range of plate stiffnesses was tested by varying the modulus of elasticity of the plate from 207 GPa to 1 GPA. Moments were applied in the plane of the plate, about the axis of the plate, and in the plane of the screws. Results showed that, for plates of typical geometry and elastic modulus under 10 GPa, the contribution to fracture gap motion occurring due to deformation in the bone was negligible compared to that contribution from deformation in the plate.

Cooke, F. W.↗

NASA NTRS1985

Decomposition and state variable feedback control of elastic robotic systems

Energy-efficient, lightweight robot arms for space applications have considerable structural flexibility. An approach to control of a class of flexible robotic systems is presented. A control law is derived which decouples the joint-angle motion from the flexible motion and, in addition, asymptotically decomposes the elastic dynamics into two subsystems. This allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertaintly in system parameters. Simulation results show that the combination of nonlinear decoupling and elastic stabilization permits rapid, accurate tracking of large joint angle commands with well damped elastic response, in spite of space vehicle motion and payload uncertainty.

Singh, S. N.↗

NASA NTRS1985

Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization

An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.

Singh, S. N.↗

NASA NTRS1986

Control of elastic robotic systems by nonlinear inversion and modal damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Singh, S. N.↗

NASA NTRS1986

Elastic robot control - Nonlinear inversion and linear stabilization

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Singh, S. N.↗

NASA NTRS1987

The effects of pin elasticity, clearance, and friction on the stresses in a pin-loaded orthotropic plate

The effects of pin elasticity, clearance, and friction on the stresses in a pin loaded orthotropic plate are studied. The effects are studied by posing the problem as a planar contact elasticity problem, the pin and the plate being two elastic bodies which interact through contact. Coulomb friction is assumed, the pin loads the plate in one of its principal material directions, and the plate is infinite in extent. A collocation scheme and interaction, in conjunction with a complex variable series solution, are used to obtain numerical results. The contact region between the plate and pin is unknown and must be solved for as part of the solution. The same is true of the region of friction induced no slip. Two pin stiffnesses, two clearance levels, two friction levels and two laminates, a (0/+ or - 45/90)s and a (02/+ or - 45)s, are studied. The effects of pin elasticity, clearance, and friction on the load capacity of the plate are assessed by comparing the load capacity of the plate with the capacity when the pin is rigid, perfectly fitting, and frictionless.

Hyer, M. W.↗

NASA NTRS1987

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

Oden, J. Tinsley↗

NASA NTRS1990

Measurements of radiated elastic wave energy from dynamic tensile cracks

The role of fracture-velocity, microstructure, and fracture-energy barriers in elastic wave radiation during a dynamic fracture was investigated in experiments in which dynamic tensile cracks of two fracture cofigurations of double cantilever beam geometry were propagating in glass samples. The first, referred to as primary fracture, consisted of fractures of intact glass specimens; the second configuration, referred to as secondary fracture, consisted of a refracture of primary fracture specimens which were rebonded with an intermittent pattern of adhesive to produce variations in fracture surface energy along the crack path. For primary fracture cases, measurable elastic waves were generated in 31 percent of the 16 fracture events observed; the condition for radiation of measurable waves appears to be a local abrupt change in the fracture path direction, such as occurs when the fracture intersects a surface flaw. For secondary fractures, 100 percent of events showed measurable elastic waves; in these fractures, the ratio of radiated elastic wave energy in the measured component to fracture surface energy was 10 times greater than for primary fracture.

Boler, Frances M.↗

NASA NTRS1993

Axisymmetric micromechanics of elastic-perfectly plastic fibrous composites under uniaxial tension loading

The uniaxial response of a continuous fiber elastic-perfectly plastic composite is modeled herein as a two-element composite cylinder. An axisymmetric analytical micromechanics solution is obtained for the rate-independent elastic-plastic response of the two-element composite cylinder subjected to tensile loading in the fiber direction for the case wherein the core fiber is assumed to be a transversely isotropic elastic-plastic material obeying the Tsai-Hill yield criterion, with yielding simulating fiber failure. The matrix is assumed to be an isotropic elastic-plastic material obeying the Tresca yield criterion. It is found that there are three different circumstances that depend on the fiber and matrix properties: fiber yield, followed by matrix yielding; complete matrix yield, followed by fiber yielding; and partial matrix yield, followed by fiber yielding, followed by complete matrix yield. The order in which these phenomena occur is shown to have a pronounced effect on the predicted uniaxial effective composite response.

Lee, Jong-Won↗

NASA NTRS1993

Elastic-plastic mixed-iterative finite element analysis: Implementation and performance assessment

An elastic-plastic algorithm based on Von Mises and associative flow criteria is implemented in MHOST-a mixed iterative finite element analysis computer program developed by NASA Lewis Research Center. The performance of the resulting elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors of 4-node quadrilateral shell finite elements are tested for elastic-plastic performance. Generally, the membrane results are excellent, indicating the implementation of elastic-plastic mixed-iterative analysis is appropriate.

Sutjahjo, Edhi↗

NASA NTRS2003

Furrow Topography and the Elastic Thickness of Ganymede's Dark Terrain Lithosphere

The effective elastic thickness of Ganymede's lithosphere tell of the satellite's thermal evolution through time. Generally it has been inferred that dark terrain, which is less tectonically deformed than grooved terrain, represents regions of cooler and thicker lithosphere [1]. The ancient dark terrain is cut by furrows, tectonic troughs about 5 to 20 km in width, which may have formed in response to large ancient impacts [1, 2]. We have applied the methods of [3] to estimate effective elastic thickness based on topographic profiles across tectonic furrows, extracted from a stereo-derived digital elevation model (DEM) of dark terrain in Galileo Regio [4]. Asymmetry in furrow topography and inferred flexure suggests asymmetric furrow fault geometry. We find effective elastic thicknesses ~0.4 km, similar to analyzed areas alongside bright grooved terrain. Data and Analysis: A broken-plate elastic model.

Pappalardo, Robert T.↗

NASA NTRS2003

Automated Finite Element Analysis of Elastically-Tailored Plates

A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.

Jegley, Dawn C.↗

NASA NTRS2003

Elastic-Plastic Thermal Stress Analysis of a High-Pressure Cryogenic Storage Tank

The thermal stresses on a cryogenic storage tank contribute strongly to the state of stress of the tank material and its ability to withstand operational stresses. These thermal stresses also affect the growth of any surface damage that might occur in the tank walls. These stresses are particularly of concern during the initial cooldown period for a new tank placed into service, and during any subsequent thermal cycles. A previous preliminary elastic analysis showed that the thermal stress on the inner wall would reach approximately 1,000MPa (145,000 psi). This stress far exceeds the ASTM specified room temperature values for both yield (170MPa) and ultimate (485 MPa) strength for 304L stainless steel. The present analysis determines the thermal stresses using an elastic-plastic model. The commercial software application ANSYS was used to determine the transient spatial temperature profile and the associated spatial thermal stress profiles in a segment of a thick-walled vessel during a typical cooldown process. A strictly elastic analysis using standard material properties for 304L stainless steel showed that the maximum thermal stress on the inner and outer walls was approximately 960 MPa (tensile) and - 270 MPa (compressive) respectively. These values occurred early in the cooldown process, but at different times, An elastic-plastic analysis showed significantly reducing stress, as expected due to the plastic deformation of the material. The maximum stress for the inner wall was approximately 225 MPa (tensile), while the maximum stress for the outer wall was approximately - 130 MPa (compressive).

Barker, J. Mark↗