Spaces of finite element differential forms

We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds., Springer 2013. v2: a few minor typos corrected. v3: a few more typo correction

Tests of propellers for Alvin side propulsion units

Full scale dynamometer tests were run on a series of unshrouded propellers in the range of propeller diameters considered practical for use on the side propulsion units of the research submarine ALVIN. Measurements taken included static thrust, torque, and RPM for various values of hydraulic power input to the driving motor. In other tests, propellers having 14 inch diameter and 20 inch pitch (the present ALVIN configuration) were compared for static thrust as follows: conventional blade shape, unshrouded; conventional blade shape in ALVIN flow-accelerating nozzle unit; square-ended blades in ALVIN nozzle unit. Recommendations are given concerning the proposed new ALVIN side propulsion units

Torque tests of a full size model of the Alvin/AUTEC emergency sphere release

Laboratory torque tests were perfoirmed using an actual emergency sphere release shaft of the type used in the research submarines ALVIN, SEA CLIFF and TURTLE. A test fixture was constructed which permitted laboratory simulation of the side (squeezing) forces applied to the release shaft came as a result of forebody buoyancy. Estimated full-scale side forces were applied to the cam by a laboratory compression testing machine, and the torque required to rotate the shaft was measured. Tests were run with contacting surfaces (a) clean and dry, (b) greased, and (c) immersed in sea water. From the test results, values of release torque were calculated for the submarines in question. Coefficient of friction values of the contrating materials (Monel K-500 on phosphor bronze) also are reported.Submitted to the Office of Naval Research under contract Ndnr-3484(00); NR 260-107

Experimental stress analysis of model of emergency forebody release device used in deep diving research submarines Alvin, Sea Cliff and Turtle

Originally issued as Reference No. 69-68, series later renamed WHOI-Technical ReportsTests were conducted on a full-scale model of the emergency forebody release used in the deep-diving submarines ALVIN, SEA CLIFF and TURTLE. The model was machined from metal to the same dimensional tolerances as the prototype. Resistance strain gages, attached to the model, permitted measurement of forces on component parts of the device. Of primary concern was the bending stress which might be set up in the release operating shaft when the submarine is submerged in an inclined position. Tests were arranged to simulate three possible conditions of loading of the release device at a 30 degree vehicle list angle: case (1) righting moment of inclined forebody resisted by release components only; case (2) righting moment resisted by release with assistance from lower guides; and (3) righting moment resisted by couple set up by release and rubber support ring. Test results show that shaft bending stresses (for ALVIN) are high (200,000 psi) for the case (1) condition, lower (400,000 - 90,000 psi) for case (2) and essentially zero for case (3). The conclusion is that the present forebody release design is adequate for all submarine attitudes encountered in normal operation, provided the vehicle has been assembled so that contact between sphere and rubber ring is assured at all times.Submitted to the Office of Naval Research under Contract Nonr-3484(00); NR 260-107

A pendulum inclinometer for use with small deep-submersibles

The authors developed a pendulum inclinometer suitable for use with small deepsubmersibles or surface craft. The instrument uses a relatively short heavy pendulum and a viscous damping system for minimizing the effects of unwanted oscilatory motion. The pendulum relative motion is transmitted to the dial pointer through a flexible cord. The mechanism is designed so that the inclinometer gives a direct reading of the tangent of the angle of inclination. Adjustments are provided for leveling the instrument and for setting the dial to zero. Upper and lower clamping devices protect the pendulum suspension from damage during transit. The inclinometer has been used successfully in recent inclining experiments for the small research submarine Alvin.Prepared for the Office of Naval Research under Contract N00014-73-C-0097; NR 083-383

Micromechanics of Spray-On Foam Insulation

Understanding the thermo-mechanical response of the Space Shuttle External Tank spray-on foam insulation (SOFI) material is critical, to NASA's Return to Flight effort. This closed-cell rigid polymeric foam is used to insulate the metallic Space Shuttle External Tank, which is at cryogenic temperatures immediately prior to and during lift off. The shedding of the SOFI during ascent led to the loss of the Columbia, and eliminating/minimizing foam lass from the tank has become a priority for NASA as it seeks to resume scheduled space shuttle missions. Determining the nature of the SOFI material behavior in response to both thermal and mechanical loading plays an important role as any structural modeling of the shedding phenomenon k predicated on knowledge of the constitutive behavior of the foam. In this paper, the SOFI material has been analyzed using the High-Fidelity Generalized Method of Cells (HFGMC) micromechanics model, which has recently been extended to admit a triply-periodic 3-D repeating unit cell (RUC). Additional theoretical extensions that mere made in order to enable modeling of the closed-cell-foam material include the ability to represent internal boundaries within the RUC (to simulated internal pores) and the ability to impose an internal pressure within the simulated pores. This latter extension is crucial as two sources contribute to significant internal pressure changes within the SOFI pores. First, gas trapped in the pores during the spray process will expand or contract due to temperature changes. Second, the pore pressure will increase due to outgassing of water and other species present in the foam skeleton polymer material. With HFGMC's new pore pressure modeling capabilities, a nonlinear pressure change within the simulated pore can be imposed that accounts for both of these sources, in addition to stmdar&-thermal and mechanical loading; The triply-periodic HFGMC micromechanics model described above was implemented within NASA GRC's MAC/GMC software package, giving the model access to a range of nonlinear constitutive models for the polymeric foam skeleton material. A repeating unit cell architecture was constructed that, while relatively simple, still accounts for the geometric anisotropy of the porous foam microstructure and its thin walls and thicker edges. With the lack of reliable polymeric foam skeleton materia1 properties, many simulations were executed aimed at backing out these material properties. Then, using these properties, predictions of the thermo-mechanical behavior of the foam, including calculated internal applied pressure profiles, were performed and compared with appropriate experimental data

An Experimental Approach to Examining Psychological Contributions to Multisite Musculoskeletal Pain.

The present study examined the prospective value of pain catastrophizing, fear of pain, and depression in the prediction of multisite musculoskeletal pain following experimentally induced delayed-onset muscle soreness (DOMS). The study sample consisted of 119 (63 females, 56 males) healthy university students. Measures of pain catastrophizing, fear of pain, and depression were completed prior to the DOMS induction procedure. Analyses revealed that pain catastrophizing and fear of pain prospectively predicted the experience of multisite pain following DOMS induction. Analyses also revealed that women were more likely to experience multisite pain than men. There was no significant relation between depressive symptoms and the experience of multisite pain. The discussion addresses the mechanisms by which pain catastrophizing and fear of pain might contribute to the spreading of pain. Clinical implications of the findings are also addressed. Perspective: The results of this experimental study suggest that pain catastrophizing and fear of pain might increase the risk of developing multisite pain following musculoskeletal injury