Neutral elastic deformations
Elastic bodies or systems may not require external energy for certain finite and continuous deformations. Conditions providing these kinds of effortless, or neutral, deformations are discussed.
Durum, M. M.↗
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The interaction of a compressible fluid and an elastically deforming boundary
Unsteady interaction of compressible fluid and flat circular deforming elastic membrane analyzed by coupled computer program method
Madden, R.↗
Origin of multi-ring basin ridge systems - An upper limit to elastic deformation based on a finite-element model
A finite-element model of a 500-km diameter lunar basin flooded with 10 km of basalt was used to represent the central portion of a multi-ring basin undergoing elastic deformation as a result of basin subsidence. Gravitational forces due to the weight of the basalt were set as the initial forces in the model; elastic constants computed from seismic velocities of lunar samples provided strength specifications. In addition, the crust was constrained by permitting no displacements at a depth of 60 km. Because of the strength of the lithosphere, surface subsidence amounted to only 20 m. This magnitude of elastic deformation does not equal that found on the lunar surface, but the orientation of principal stress and the position of circumferential compressional stress are compatible with the evolution of inner-ring and radial ridge systems by gravitational-induced downdropping.
Maxwell, T. A.↗
Elastically Deformable Side-Edge Link for Trailing-Edge Flap Aeroacoustic Noise Reduction
A system is provided for reducing aeroacoustic noise generated by an aircraft having wings equipped with trailing-edge flaps. The system includes a plurality of elastically deformable structures. Each structure is coupled to and along one of the side edges of one of the trailing-edge flaps, and is coupled to a portion of one of the wings that is adjacent to the one of the side edges. The structures elastically deform when the trailing-edge flaps are deployed away from the wings.
Khorrami, Mehdi R.↗
Large elastic deformations of shells with the inclusion of transverse normal strain
Large elastic deformations of incompressible materials shells with inclusion of transverse normal strain, considering thickness change at boundaries
Biricikoglu, V.↗
Elastic deformation of the gyro rotor in the relativity gyro experiment
The elastic deformation of a spinning sphere is calculated from first principles. Numerical results are quoted for a quartz sphere spinning at 200 Hz, the most likely configuration for the relativity gyro experiment. The difference in principal moments of inertia is also calculated for the spinning gyro.
Eby, P. B.↗
Closed-form analysis for elastic deformations of multilayered strands
Closed-form solutions are developed for elastic deformation characteristics of multilayered strands under tensile and torsional loads. These analytical results are successfully applied to obtain expressions for the effective extensional and torsional moduli of rigidity for the strands. Finally, a simple design criterion is established for 'nonrotating' cables.
Kumar, K.↗
Elastic deformation of ball bearings, gears, and cams
Simplified technique aids designers in calculation of elastic deformation at center of contact area for ball bearings, gears, cams, and similar components.
Hamrock, B. J.↗
Thermal elastic deformations of the planet Mercury
The variation in solar heating due to the resonance rotation of Mercury produces periodic elastic deformations on the surface of the planet. The thermal stress and strain fields under Mercury's surface are calculated after certain simplifications. It is shown that deformations penetrate to a greater depth than the variation of solar heating, and that the thermal strain on the surface of the planet pulsates with an amplitude of 0.004 and a period of 176 days.
Liu, H.↗
Thermal elastic deformations of the planet Mercury.
The variation in solar heating due to the resonance rotation of Mercury produces periodic elastic deformations on the surface of the planet. The thermal stress and strain fields under Mercury's surface are calculated after certain simplifications. It is found that deformations penetrate to a greater depth than the variation of solar heating, and that the thermal strain on the surface of the planet pulsates with an amplitude of .004 and a period of 176 days.
Liu, H.-S.↗
The fabrication of toroidal and coma-corrected toroidal diffraction gratings from spherical master gratings using elastically-deformable substrates - A progress report
A technique has been developed which permits toroidal, and coma-corrected toroidal, diffraction gratings to be replicated from spherical master gratings by the use of elastically-deformable substrates. Toroidal gratings correct for astigmatism and, thus, make it possible to construct stigmatic spectrometers that employ a single reflective diffraction grating. These spectrometers are particularly useful for the extreme-ultraviolet (EUV) wavelength range, where reflection coefficients are low, since the single optical surface provides for dispersion, focusing, and astigmatism correction. The fabrication procedures for the pure toroidal, and coma-corrected toroidal, gratings are described, and initial test results are presented. The use of the toroidal gratings in a high-resolution sounding-rocket EUV spectroheliometer, and in both the coronal diagnostics spectrometer and the ultraviolet coronagraph spectrometer on the ESA/NASA solar and heliospheric observatory mission, is described briefly, and the use of this technique for the fabrication of a coma-corrected toroidal grating for the prime Rowland spectrograph of the FUSE/Lyman mission is briefly discussed.
Huber, Martin C. E.↗
Short and medium range structure in elastic deformation of metallic and covalent glasses
Here, we present a concise methodology to analyze structural response to the applied stress in amorphous solids, including metallic glasses (MG), glassy selenium, silica and polycarbonate, using high energy x-ray diffraction and atomic pair distribution function (PDF) analysis. To assess the structural anisotropy induced by applied axial stress, diffraction data were expanded into spherical harmonics. Using Bessel transformation, components of the structure function were converted into isotropic and anisotropic PDFs. The PDFs were compared to the expected model behavior for ideal elastic deformation to separate homogeneous affine strain from local non-affine strains. In metallic glass the range of non-affine deformation is limited to the nearest neighbor shell, suggesting local strain relaxation under stress that occurs even in the elastic regime. Beyond the second atomic shell strain is uniform. However, in glassy silica, polycarbonate and selenium strong local bonding inhibits local displacements and strain in short range order is accommodated by rotation of local units. Interestingly, beyond a molecular unit, deformation in covalent systems is similar to MG, and response of the medium range order scales with the macroscopic stress.
glassy structure↗
A numerical analysis of contact and limit-point behavior in a class of problems of finite elastic deformation
Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.
Endo, T.↗
Numerical evaluation of the surface deformation of elastic solids subjected to a hertzian contact stress
The elastic deformation of two ellipsoidal solids in contact and subjected to Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure is applied over each rectangular area. The influence of the size of the rectangular area upon accuracy was also studied. The results indicate the distance from the center of the contact at which elastic deformation becomes insignificant.
Hamrock, B. J.↗
Numerical evaluation of the surface deformation of elastic solids subjected to a Hertzian contact stress
The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study was made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.
Dowson, D.↗
Numerical evaluation of the surface deformation of elastic solids subjected to a Hertzian contact stress
The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution has been evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study has been made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.
Dowson, D.↗
Elastic deformation, plasticity, and fracture in granular compaction
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Clemmer, Joel Thomas [Sandia National Laboratories↗
Incremental analysis of large elastic deformation of a rotating cylinder
The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.
Buchanan, G. R.↗