Static deformation of silica and silicates
Static ductile deformational processes in deformed quartz, olivine, pyroxenes, and plagioclase
Carter, N. L.↗
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Static deformation of silica and silicates
Static ductile deformation in quartz, olivine, pyroxenes and placioglase, noting plastic deformation and recovery
Carter, N. L.↗
Optimum placement of controls for static deformations of space structures
Many large space structures, such as large antennas, have to maintain a fairly exact shape to operate satisfactorily. Such structures require active and passive controls to maintain their accurate shape under disturbances. The present paper is concerned with optimum placement of controls for correcting static deformations. Both force actuators and heaters are considered for controls. A formulation of design against the worst disturbance is derived. A beam example is employed to demonstrate the procedure.
Haftka, R. T.↗
Optimum placement of controls for static deformations of space structures
The placement of thermal or force actuators to control slowly varying disturbances in the shape of large space structures is investigated analytically. Expressions are derived based on disturbances defined as the worst linear combination of a given set of functions and minimized numerically using the NEWSUMT optimization package. Results are presented in tables and graphs for a free-free beam with equidistant controls and polynomial-form (order 2-6) disturbances. Control placement is found to be of greater importance for force actuators, but is also of significance for thermal actuators.
Haftka, R. T.↗
Analytical estimation for static deformation of wire ropes with fibrous core
This paper develops closed-form solutions for the extension of twisted wire ropes with fibrous cores which are subjected to axial forces as well as axial moments. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of wire ropes with fibrous core is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.
Kumar, K.↗
Effect of static deformation and external forces on the oscillations of levitated droplets
The oscillations of an aspherical droplet subjected to different external forces are considered. For an arbitrary shape deformation, it is shown that the frequency spectrum splits into (2l - 1) peaks for a mode l oscillation, and the splitting of the frequency spectrum is calculated for mode 2, 3, and 4 oscillations. The deformation is then treated as a consequence of a general external force, and the frequency split is obtained in terms of the external force parameters. Droplets levitated by acoustic, electromagnetic, and combined acoustic-electromagnetic forces are considered in particular, and it is shown that the effects of asphericity adequately explain the splitting of the frequency spectrum observed commonly in experiments. The interpretation of spectra with regard to accurate surface tension measurement using the oscillations of levitated droplets is discussed, and the results applied to some previous experimental results. It is shown that the accuracy of surface tension measurements can improve if the asphericity caused by the levitating force, and the resulting frequency split, are taken into account.
Suryanarayana, P. V. R.↗
Statics of deformable solids.
Text on deformable solid statics including indeterminate systems, strain, stress, elasticity, continuum energy, plasticity and mathematical appendix
STATIC DEFORMATION↗
Linear and Geometrically Nonlinear Structural Shape Sensing from Strain Data
An aircraft’s shape must be measured during flight to implement active shape controls such as active trim shape, divergence, and sonic boom controls. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, and/or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration X-59 aircraft. A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3%prediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data are also demonstrated in this study using the X-59 aircraft. Predicted structural deformations match reasonably with the target deformations, even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.
Static Deformation↗
Structural Shape Sensing from Strain Data Using the Basis Function Method
An aircraft shape must be measured during flight to implement an active trim shape control, such as an active dihedral control for a highly flexible aircraft with a high-aspect-ratio wing, and an active sonic boom control for a supersonic transport aircraft. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration Low Boom Flight Demonstration mission X-59 Quiet Supersonic Technology (QueSST) aircraft (Lockheed Martin, Bethesda, Maryland). A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3-percentprediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data is also demonstrated in this study using the X-59 QueSST aircraft. Predicted structural deformations match reasonably with the target deformations even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.
Chan-gi Pak↗
The pressure dependence of the elastic constants of cubic crystals in the NaCl and spinel structures from a lattice model
Homogeneous static deformation method crystals in NaCl and spinel structures using homogeneous static deformation method
Sammis, C. G.↗
The dynamic response of composite beams to axial impact
Large deformation response of simple composite structural elements to intense dynamic loadings is studied by focusing on the response of beams. Overall goals are to: design a simple test fixture to introduce crash related bending loads in beams; determine any difference between large deformation static and large deformation dynamic response; determine the influence of laminate stacking arrangements on the dynamic response, failure mode, and energy absorbed; and predict the dynamic response. Twelve different laminate orientations were investigated. Modeling of the response was done with an existing finite element program. The program computed nonlinear transient response analysis of a structure objected to a time varying load.
Derian, E. J.↗
An investigation of the vibration characteristics of shrouded-bladed-disk rotor stages
Coupled differential equations of motion are given for application to a rotating, pretwisted and heated beam under the effects of thermal stresses and gas bending loads. The circumferential modes of the multi-blade vibration of a bladed-disk rotor stage were studied. A finite element method was developed for the dynamic and static deformation analysis of the blade. The deformations of a bladed disk and a shrouded-bladed disk were studied by introducing a special bladed-disk element and a special shrouded-blade element. Some features of the vibration of part-span-shrouded, bladed-disk rotor stages are discussed. The static deformation, thermal stress and gas bending effects on the blade vibration were presented previously.
Chen, L.-T.↗
Analytical solutions for static elastic deformations of wire ropes
This paper develops closed-form solutions for extension of twisted wire ropes subjected to axial forces for two different end conditions. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of the wire ropes is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.
Kumar, K.↗
Transition Analysis for the Pazy Wing
The Pazy wing, designed as a benchmark for highly flexible wings that experience large deformations, presents intriguing nonlinear phenomena due to its unique geometry with spanwise varying static deformation and low Reynolds number flow conditions. These phenomena include limit cycle oscillation related to laminar separation bubbles, boundary-layer transition, and dynamic stall. The primary focus of this study is to investigate transition behavior on the sagged Pazy wing under static loading by using the shear-stress-transport (SST)-based Langtry-Menter 𝜸 − 𝑹𝒆𝜽𝒕 transition model in the NASA OVERFLOW and FUN3D solvers. Based on the steady-state results obtained via different variants of the Langtry-Menter model, we investigate the likely transition behavior over a range of incidence angles. The predicted flowfield on the sagged Pazy wing is strongly three dimensional and the application of turbulence index as a viable indicator of the transition front in such flows is also explored. The study demonstrates the limitations of the Langtry-Menter model when applied to low Reynolds number flows. We introduce a spanwise periodic configuration to simulate a narrow-span section of the Pazy wing, specifically centered on one of the 14 nearly equidistant ribs spanning the wing. The computational results demonstrate that the spanwise periodic configuration provides a straightforward environment for studying transition characteristics as well as demonstrating systematic grid convergence and successful code-to-code comparisons. The research offers useful insights into the transition characteristics of flexible wings under various loading conditions, contributing to the field of aeroelastic simulations.
CFD Modeling↗
Transition Analysis for the Pazy Wing
The Pazy wing, designed as a benchmark for highly flexible wings that experience large deformations, presents intriguing nonlinear phenomena due to its unique geometry with spanwise varying static deformation and low Reynolds number flow conditions. These phenomena include limit cycle oscillation related to laminar separation bubbles, boundary-layer transition, and dynamic stall. The primary focus of this study is to investigate transition behavior on the sagged Pazy wing under static loading by using the shear-stress-transport (SST)-based Langtry-Menter 𝜸 − 𝑹𝒆𝜽𝒕 transition model in the NASA OVERFLOW and FUN3D solvers. Based on the steady-state results obtained via different variants of the Langtry-Menter model, we investigate the likely transition behavior over a range of incidence angles. The predicted flowfield on the sagged Pazy wing is strongly three dimensional and the application of turbulence index as a viable indicator of the transition front in such flows is also explored. The study demonstrates the limitations of the Langtry-Menter model when applied to low Reynolds number flows. We introduce a spanwise periodic configuration to simulate a narrow-span section of the Pazy wing, specifically centered on one of the 14 nearly equidistant ribs spanning the wing. The computational results demonstrate that the spanwise periodic configuration provides a straightforward environment for studying transition characteristics as well as demonstrating systematic grid convergence and successful code-to-code comparisons. The research offers useful insights into the transition characteristics of flexible wings under various loading conditions, contributing to the field of aeroelastic simulations.
CFD Modeling↗
Control of micromachined deformable mirrors
A micromachined deformable mirror with pixelated electrostatic actuators is proposed. The paper begins with a physical description of the proposed mirror. Then a mathematical model in the form of a nonlinear partial differential equation describing the mirror surface deformations is derived. This model is used to derive the required voltages for the actuators to achieve a specified static deformation of the mirror surface. This is followed by the derivation of a static nonlinear feedback controller for achieving noninteracting actuation. Then the structure for a complete control system for wavefront correction is proposed. The paper concludes with a discussion of the physical implementation of the proposed control system.
Agronin, M. L.↗
Control of Micromachined Deformable Mirrors
A micromachined deformable mirror with pixelated electrostatic actuators is proposed. The paper begins with a physical description of the proposed mirror. Then, a mathematical model in the form of a nonlinear partial differential equation describing the mirror surface deformations is derived. This model is used to derive the required voltages for the actuators to achieve a specified static deformation of the mirror surface. This is followed by the derivation of a static nonlinear feedback controller for achieving noninteracting actuation. Then, the structure for a complete control system for wavefront correction is proposed. The paper concludes with a discussion of the physical implementation of the proposed control system.
mirrors↗
Deformation of silicates in some Fra Mauro breccias.
The results of the studies conducted show that there is no unequivocal evidence for appreciable static deformation (other than annealing) in the Fra Mauro formation. These rocks probably have been derived from depths to about 10 km. It is suggested that there has been no substantial tectonic activity in the range from the surface to 10 km since these rocks and those of the other Apollo sites crystallized some 3 to 4 billion years ago. This negative conclusion implies that at least the outer layer of the moon has been static for this length of time.
Lallemant, H. G. A.↗