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NASTRAN program differential stiffness method applied to structural analysis of Apollo Telescope Mount solar array wing and results compared with static load tests
Large dispacement assumed-mode modeling techniques are examined in the context of multibody elastodynamics. The range of both general and element-specific approaches are studied with the aid of examples involving beams, plates, and shells. For systems undergoing primarily structural bending and twisting with little or no membrane distortion, it is found that fully-linear, element-specific, modal formulations provide the most accurate time history solutions at the least expense. When membrane effects become dominant in structural problems due to loading and boundary conditions, one must naturally resort to a formulation involving a nonlinear stress-strain relationship in addition to nonlinear terms associated with large overall system motion. Such nonlinear models were investigated using assumed modes and found to lead to modal convergence difficulties when standard free-free structural modes are employed. A constrained mode formulation aimed at addressing the convergence problem is proposed.
Large-displacement elastic and elastic-plastic, finite-element stress-strain analyses of an oxygen-tree high-conductivity (OFHC) copper plate specimen were performed using an updated Lagrangian formulation. The plate specimen is intended for low-cost experiments that emulate the most important thermomechanical loading and failure modes of a more complex rocket nozzle. The plate, which is loaded in bending at 593 C, contains a centrally located and internally pressurized channel. The cyclic crack initiation lives were estimated using the results from the analyses and isothermal strain-controlled low-cycle fatigue data for OFHC copper. A comparison of the predicted and experimental cyclic lives showed that an elastic analysis predicts a longer cyclic life than that observed in experiments by a factor greater than 4. The results from elastic-plastic analysis for the plate bend specimen, however, predicted a cyclic life in close agreement with experiment, thus justifying the need for the more rigorous stress-strain analysis.
The use of linear rigid formats in COSMIC NASTRAN without DMAP procedures for the analysis of nonlinear propeller structures is described. Approaches for updating geometry and applying follower forces for incremental loading are demonstrated. The COSMIC NASTRAN rigid formats and other independent finite element programs are compared. The comparisons include results from the four approaches for updating the geometry using RIGID FORMAT 1, RIGID FORMATS 4 and 13, MARC and MSC/NASTRAN. It is shown that user friendly updating approaches can be used to predict the large displacements and instability of these nonlinear structures. The approaches are easily implemented by the user and predict conservative results.
The use of linear rigid formats in COSMIC NASTRAN without DMAP procedures for the analysis of nonlinear propeller structures is described. Approaches for updating geometry and applying follower forces for incremental loading are demonstrated. Comparisons are made with COSMIC NASTRAN rigid formats and other independent finite element programs. Specifically, the comparisons include results from the four approaches for updating the geometry using RIGID FORMAT 1, RIGID FORMATS 4 and 13, MARC and MSC/NASTRAN. It is shown that 'user friendly' updating approaches (without DMAPS) can be used to predict the large displacements and instability of these nonlinear structures. These user friendly approaches can be easily implemented by the user and predict conservative results.
A total Lagrangian finite element formulation for the deformable bodies in multibody mechanical systems that undergo finite relative rotations is developed. The deformable bodies are discretized using finite element methods. The shape functions that are used to describe the displacement field are required to include the rigid body modes that describe only large translational displacements. This does not impose any limitations on the technique because most commonly used shape functions satisfy this requirement. The configuration of an element is defined using four sets of coordinate systems: Body, Element, Intermediate element, Global. The body coordinate system serves as a unique standard for the assembly of the elements forming the deformable body. The element coordinate system is rigidly attached to the element and therefore it translates and rotates with the element. The intermediate element coordinate system, whose axes are initially parallel to the element axes, has an origin which is rigidly attached to the origin of the body coordinate system and is used to conveniently describe the configuration of the element in undeformed state with respect to the body coordinate system.
As the development in flexible space structures expands, the need for an efficient and accurate suspension system for ground tests increases accordingly. In this article, a disk suspension system was developed. Analytical results describing the dynamics of a passive and active suspension system were generated given realistic parameters of the system. These results for the passive case, were then compared with the data obtained from an experimental model with initial displacement and random forcing inputs. The dynamics of the system was analyzed. Results show that the experimental model resembles closely the analytical model and therefore strongly suggests feasibility of such a suspension system.
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Gravity-off-loading of deployable spacecraft mechanisms during ground testing is a long-standing problem. Deployable structures which are usually too weak to support their own weight under gravity require a means of gravity-off-loading as they unfurl. Conventional solutions to this problem have been helium-filled balloons or mechanical pulley/counterweight systems. These approaches, however, suffer from the deleterious effects of added inertia or friction forces. The changing form factor of the deployable structure itself and the need to track the trajectory of the center of gravity also pose a challenge to these conventional technologies. This paper presents a novel testing apparatus for high-fidelity zero-gravity simulation for special application to deployable space structures such as solar arrays, magnetometer booms, and robotic arms in class 100,000 clean room environments
Development of computer programs for nonlinear structural analyses has progressed from special application programs to large, generalized programs. AGGIE I program is moderately-sized finite-element program that was developed specifically for nonlinear structural analysis. It is based on two- and three-dimensional isoparametric solid elements. AGGIE I accounts for nonlinearities due to large displacements, large strains and non-linear material behavior.
Noninvasive device measures large amplitudes at low frequencies. Low-angle, light-sensitive system tracks moving leading edge of model. Applications include opening and closing of automatic doors as far and fast as needed.
A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.
Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.
Two methods of analysis have been developed for legged planetary landers. The first of these, the Large Displacement Gear Analysis, is a design tool for statically determining the large displacement stroking behavior, energy absorption characteristics, and internal load distributions in a single gear. The second, the Landing Dynamics Analysis, predicts the spatial landing dynamics of a legged lander. Effects of structural flexibility, elastic-plastic gear load characteristics, and soil properties on the loads, motions, and stability of the lander may be determined. Validation of the analytical techniques is accomplished through comparison of predicted results and experimental data obtained during a model test program.
Finite element thermal-structural analyses of large, cable-stiffened space structures are presented. A computational scheme for the calculation of prestresses in the cable-stiffened structures is also described. The determination of thermal loads on orbiting space structures due to environment heating is discussed briefly. Three finite element structural analysis techniques are presented for the analysis of prestressed structures. Linear, stress stiffening, and large displacement analysis techniques were investigated. These three techniques were employed for analysis of prestressed cable structures at different prestress levels. The analyses produced similar results at small prestress, but at higher prestress, differences between the results became significant. For the cable-stiffened structures studied, the linear analysis technique may not provide acceptable results. The stress stiffening analysis technique may yield results of acceptable accuracy depending upon the level of prestress. The large displacement analysis technique produced accurate results over a wide range of prestress and is recommended as a general analysis technique for thermal-structural analysis of cable-stiffened space structures.
The single-cantilevered beam test (SCB) is currently being considered for standardization for measuring the opening mode fracture toughness of sandwich structures subjected to facesheet-to-core separation. At present, the Area method is considered the benchmark method for determining energy required to propagate the crack. This method is problematic since it requires periodic unloading and cannot be evaluated instantaneously. Therefore, a method is needed to accurately and instantaneously calculate opening mode fracture toughness. In previous work, SCB tests with thin-gauge facesheets were performed to compare the J-integral approach to data reduction methods including the Modified Beam Theory (MBT) and the Area method. Large deviations (over 10%) in the calculated fracture toughness were observed between the J-integral and MBT for large displacements. In this study, a simulated SCB experiment using a virtual crackclosure technique was performed to assess the previously observed discrepancies. The predicted load displacement response, the predicted angle at the load application point, and the predicted crack growth results are in good agreement (within 5%) with the corresponding experimental data. Using the predicted load and angles, the predicted J-integral is in good agreement (within 10%) with the experimentally obtained solution. Using the MBT approach, the previously observed deviations in the fracture toughness were determined to be associated with the empirical extrapolation procedure to estimate the crack-root rotation correction from nonlinear compliance curves. The nonlinear compliance is determined to be associated with large displacement effects observed within the predicted and experimental results.
In September 1987 research at Cornell levitated a small rotor on superconducting bearing at 10,000 rpm. In April 1989 a speed of 120,000 rpm was achieved in a passive bearing with no active control. The bearing material used was YBa2Cu3O7. There is no evidence that the rotation speed has any significant effect on the lift force. Magnetic force measurements between a permanent rare-earth magnet and high T(sub c) superconducting material versus vertical and lateral displacements were made. A large hysteresis loop results for large displacements, while minor loops result for small displacements. These minor loops seem to give a slope proportional to the magnetic stiffness, and are probably indicative of flux pinning forces. Experiments of rotary speed versus time show a linear decay in a vacuum. Measurements of magnetic drag forces of a magnetic dipole over a high-T(sub c) superconducting disc of YBCO show that the drag force reaches a constant value, independent of the speed. Dampling of lateral vibrations of levitated rotors were measured which indicates that transverse flux motion in the superconductor will create dissipation. As a result of these force measurements, an optimum shape for the superconductor bearing pads which gives good lateral and axial stability was designed. Recent force measurements on melt-quench processed superconductors indicate a substantial increase in levitation force and magnetic stiffness over free sintered materials. As a result, application of high-T(sub c) superconducting bearings are beginning to show great promise at this time.
The lateral restoring force on a magnet levitated above a superconductor is calculated as a function of displacement from its original position at rest using Bean's critical-state model to describe flux pinning. The force is linear for small displacements and saturates at large displacements. In the absence of edge effects the force always attracts the magnet to its original position. Thus it is a restoring force that contributes to the stability of the levitated magnet. In the case of a thick superconductor slab, the origin of the force is a magnetic dipole layer consisting of positive and negative supercurrents induced on the trailing side of the magnet. The qualitative behavior is consistent with experiments reported to date. Effects due to the finite thickness of the superconductor slab and the granular nature of high-Tc materials are also considered.