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NASA NTRS1989

Crack-face displacements for embedded elliptic and semi-elliptical surface cracks

Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

Raju, I. S.↗

NASA NTRS1990

Crack-face displacements for an embedded elliptic crack in an infinite solid subjected to arbitrary tractions

Analytical expression for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary traction are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

Raju, I. S.↗

NASA NTRS1929

The comparative performance of Roots type aircraft engine superchargers as affected by change in impeller speed and displacement

This report presents the results of tests made on three sizes of roots type aircraft engine superchargers. The impeller contours and diameters of these machines were the same, but the length were 11, 8 1/4, and 4 inches, giving displacements of 0.509, 0.382, and 0.185 cubic foot per impeller revolution. The information obtained serves as a basis for the examination of the individual effects of impeller speed and displacement on performance and of the comparative performance when speed and displacement are altered simultaneously to meet definite service requirements. According to simple theory, when assuming no losses, the air weight handled and the power required for a given pressure difference are directly proportional to the speed and the displacement. These simple relations are altered considerably by the losses. When comparing the performance of different sizes of machines whose impeller speeds are so related that the same service requirements are met, it is found that the individual effects of speed and displacement are canceled to a large extent, and the only considerable difference is the difference in the power losses which decrease with increase in the displacement and the accompanying decrease in speed. This difference is small in relation to the net power of the engine supercharger unit, so that a supercharger with short impellers may be used in those applications where the space available is very limited with any considerable sacrifice in performance.

Ware, Marsden↗

NASA NTRS2003

Development of Displacement Gages Exposed to Solid Rocket Motor Internal Environments

The Space Shuttle Reusable Solid Rocket Motor (RSRM) has three non-vented segment-to-segment case field joints. These joints use an interference fit J-joint that is bonded at assembly with a Pressure Sensitive Adhesive (PSA) inboard of redundant O-ring seals. Full-scale motor and sub-scale test article experience has shown that the ability to preclude gas leakage past the J-joint is a function of PSA type, joint moisture from pre-assembly humidity exposure, and the magnitude of joint displacement during motor operation. To more accurately determine the axial displacements at the J-joints, two thermally durable displacement gages (one mechanical and one electrical) were designed and developed. The mechanical displacement gage concept was generated first as a non-electrical, self-contained gage to capture the maximum magnitude of the J-joint motion. When it became feasible, the electrical displacement gage concept was generated second as a real-time linear displacement gage. Both of these gages were refined in development testing that included hot internal solid rocket motor environments and simulated vibration environments. As a result of this gage development effort, joint motions have been measured in static fired RSRM J-joints where intentional venting was produced (Flight Support Motor #8, FSM-8) and nominal non-vented behavior occurred (FSM-9 and FSM-10). This data gives new insight into the nominal characteristics of the three case J-joint positions (forward, center and aft) and characteristics of some case J-joints that became vented during motor operation. The data supports previous structural model predictions. These gages will also be useful in evaluating J-joint motion differences in a five-segment Space Shuttle solid rocket motor.

Bolton, D. E.↗

NASA NTRS2006

Calculation of Thermally-Induced Displacements in Spherically Domed Ion Engine Grids

An analytical method for predicting the thermally-induced normal and tangential displacements of spherically domed ion optics grids under an axisymmetric thermal loading is presented. A fixed edge support that could be thermally expanded is used for this analysis. Equations for the displacements both normal and tangential to the surface of the spherical shell are derived. A simplified equation for the displacement at the center of the spherical dome is also derived. The effects of plate perforation on displacements and stresses are determined by modeling the perforated plate as an equivalent solid plate with modified, or effective, material properties. Analytical model results are compared to the results from a finite element model. For the solid shell, comparisons showed that the analytical model produces results that closely match the finite element model results. The simplified equation for the normal displacement of the spherical dome center is also found to accurately predict this displacement. For the perforated shells, the analytical solution and simplified equation produce accurate results for materials with low thermal expansion coefficients.

Soulas, George C.↗

NASA NTRS2007

Displacement Theories for In-Flight Deformed Shape Predictions of Aerospace Structures

Displacement theories are developed for a variety of structures with the goal of providing real-time shape predictions for aerospace vehicles during flight. These theories are initially developed for a cantilever beam to predict the deformed shapes of the Helios flying wing. The main structural configuration of the Helios wing is a cantilever wing tubular spar subjected to bending, torsion, and combined bending and torsion loading. The displacement equations that are formulated are expressed in terms of strains measured at multiple sensing stations equally spaced on the surface of the wing spar. Displacement theories for other structures, such as tapered cantilever beams, two-point supported beams, wing boxes, and plates also are developed. The accuracy of the displacement theories is successfully validated by finite-element analysis and classical beam theory using input-strains generated by finite-element analysis. The displacement equations and associated strain-sensing system (such as fiber optic sensors) create a powerful means for in-flight deformation monitoring of aerospace structures. This method serves multiple purposes for structural shape sensing, loads monitoring, and structural health monitoring. Ultimately, the calculated displacement data can be visually displayed to the ground-based pilot or used as input to the control system to actively control the shape of structures during flight.

Ko, William L.↗

NASA NTRS2009

Further Development of Ko Displacement Theory for Deformed Shape Predictions of Nonuniform Aerospace Structures

The Ko displacement theory previously formulated for deformed shape predictions of nonuniform beam structures is further developed mathematically. The further-developed displacement equations are expressed explicitly in terms of geometrical parameters of the beam and bending strains at equally spaced strain-sensing stations along the multiplexed fiber-optic sensor line installed on the bottom surface of the beam. The bending strain data can then be input into the displacement equations for calculations of local slopes, deflections, and cross-sectional twist angles for generating the overall deformed shapes of the nonuniform beam. The further-developed displacement theory can also be applied to the deformed shape predictions of nonuniform two-point supported beams, nonuniform panels, nonuniform aircraft wings and fuselages, and so forth. The high degree of accuracy of the further-developed displacement theory for nonuniform beams is validated by finite-element analysis of various nonuniform beam structures. Such structures include tapered tubular beams, depth-tapered unswept and swept wing boxes, width-tapered wing boxes, and double-tapered wing boxes, all under combined bending and torsional loads. The Ko displacement theory, combined with the fiber-optic strain-sensing system, provide a powerful tool for in-flight deformed shape monitoring of unmanned aerospace vehicles by ground-based pilots to maintain safe flights.

Ko, William L.↗

NASA NTRS2012

Method of Bonding Optical Elements with Near-Zero Displacement

The International X-ray Project seeks to build an x-ray telescope using thousands of pieces of thin and flexible glass mirror segments. Each mirror segment must be bonded into a housing in nearly perfect optical alignment without distortion. Forces greater than 0.001 Newton, or displacements greater than 0.5 m of the glass, cause unacceptable optical distortion. All known epoxies shrink as they cure. Even the epoxies with the least amount of shrinkage (<0.01%) cause unacceptable optical distortion and misalignment by pulling the mirror segments towards the housing as it cures. A related problem is that the shrinkage is not consistent or predictable so that it cannot be accounted for in the setup (i.e., if all of the bonds shrunk an equal amount, there would be no problem). A method has been developed that allows two components to be joined with epoxy in such a way that reduces the displacement caused by epoxy shrinking as it cures to less than 200 nm. The method involves using ultraviolet-cured epoxy with a displacement sensor and a nanoactuator in a control loop. The epoxy is cured by short-duration exposures to UV light. In between each exposure, the nano-actuator zeroes out the displacement caused by epoxy shrinkage and thermal expansion. After a few exposures, the epoxy has cured sufficiently to prevent further displacement of the two components. Bonding of optical elements has been done for many years, but most optics are thick and rigid elements that resist micro-Newton-level forces without causing distortion. When bonding thin glass optics such as the 0.40-mm thick IXO X-ray mirrors, forces in the micro- and milli-Newton levels cause unacceptable optical figure error. This innovation can now repeatedly and reliably bond a thin glass mirror to a metal housing with less than 0.2 m of displacement (<200 nm). This is an enabling technology that allows the installation of virtually stress-free, undistorted thin optics onto structures. This innovation is applicable to the bonding of thin optical elements, or any thin/flexible structures, that must be attached in an undistorted, consistent, and aligned way.

Robinson, David↗

NASA NTRS2014

Modified Displacement Transfer Functions for Deformed Shape Predictions of Slender Curved Structures with Varying Curvatives

To eliminate the need to use finite-element modeling for structure shape predictions, a new method was invented. This method is to use the Displacement Transfer Functions to transform the measured surface strains into deflections for mapping out overall structural deformed shapes. The Displacement Transfer Functions are expressed in terms of rectilinearly distributed surface strains, and contain no material properties. This report is to apply the patented method to the shape predictions of non-symmetrically loaded slender curved structures with different curvatures up to a full circle. Because the measured surface strains are not available, finite-element analysis had to be used to analytically generate the surface strains. Previously formulated straight-beam Displacement Transfer Functions were modified by introducing the curvature-effect correction terms. Through single-point or dual-point collocations with finite-elementgenerated deflection curves, functional forms of the curvature-effect correction terms were empirically established. The resulting modified Displacement Transfer Functions can then provide quite accurate shape predictions. Also, the uniform straight-beam Displacement Transfer Function was applied to the shape predictions of a section-cut of a generic capsule (GC) outer curved sandwich wall. The resulting GC shape predictions are quite accurate in partial regions where the radius of curvature does not change sharply.

displacement transfer functions↗

NASA NTRS2015

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

displacement transfer functions↗

NASA NTRS2017

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

displacement theory↗

DOE OSTI2024

Measurements of displacement cross sections of metals for 120-GeV proton beam irradiation

The number of displacements per atom (dpa) is widely used as an indicator of irradiation damage of materials in proton accelerator facilities. Experiments have been carried out to validate the dpa of metallic materials for protons with energies below 3 GeV. However, measurements of the displacement cross-sections for high-energy protons above 3 GeV have not been carried out and the calculations have not been validated. To validate the displacement cross section of metals in high-energy region, electrical resistivity changes in wires of aluminum, copper and tungsten at 8 K were measured using protons with energies of 120-GeV. The results show that the Norgett-Robinson-Torrens dpa model of the Particle and Heavy Ion Transport Calculation Code overestimates the experimental data. On the other hand, the calculated results using the athermal recombination corrected dpa model were in agreement with the measured displacement cross sections. In the proton energy region above 1 GeV, the displacement cross section is almost constant, which is due to the fact that the damage energy of the material under 1 GeV proton irradiation is almost the same as under 120 GeV proton irradiation. Damage recovery of defects accumulated in the sample was also measured using isochronal annealing: At 80 K, approximately 60 % and 80 % of the damage remains for copper and tungsten, respectively. These results are the same as those obtained from other experiments on proton and neutron irradiation.

43 PARTICLE ACCELERATORS↗

NASA NTRS2006

A low cost imaging displacement measurement system for spacecraft thermal vacuum testing

A low cost imaging displacement technique suitable for use in thermal vacuum testing was built and tested during thermal vacuum testing of the space infrared telescope facility (SIRTF, later renamed Spitzer infrared telescope facility). The problem was to measure the relative displacement of different portions of the spacecraft due to thermal expansion or contraction. Standard displacement measuring instrumentation could not be used because of the widely varying temperatures on the spacecraft and for fear of invalidating the thermal vacuum testing. The imaging system was conceived, designed, purchased, and installed in approximately 2 months at very low cost. The system performed beyond expectations proving that sub millimeter displacements could be measured from over 2 meters away. Using commercial optics it was possible to make displacement measurements down to 10 (mu)m. An automated image processing tool was used to process the data, which not only speeded up data reduction, but showed that velocities and accelerations could also be measured. Details of the design and capabilities of the system are discussed along with the results of the test on the observatory. Several images from the actual test are presented.

thermal vacuum↗

DOE OSTI2025

Search for displaced leptons in $\sqrt{𝑠}$ =13 TeV and 13.6 TeV 𝑝⁢𝑝 collisions with the ATLAS detector

A search for leptons displaced from the primary vertex is performed with the ATLAS detector at the Large Hadron Collider. The search includes the full proton-proton collision dataset collected during Run 2 at $\sqrt{𝑠}$ = 13 TeV and a partial dataset collected during Run 3 in 2022–2023 at $\sqrt{𝑠}$ = 13.6 TeV, corresponding to integrated luminosities of 140 fb −1 and 56.3 fb −1 , respectively. Final states with displaced electrons or muons are considered, and novel triggers introduced in Run 3 are employed that use large impact parameter tracking to reconstruct displaced tracks with low momentum. In addition, photon reconstruction and multivariate techniques are employed to broaden the sensitivity to channels with large background rates or highly displaced electrons, respectively. The results are consistent with the Standard Model background expectations and are used to set model-independent limits on the production of displaced electrons and muons. The analysis is also interpreted in the context of a gauge-mediated supersymmetry breaking model with pair-produced long-lived sleptons and a dark sector model with pair-produced chargino-like states. The results include 95% confidence level exclusions of selectrons with lifetimes from 4 ps to 60 ns and a mass of 150 GeV, and exclusions of selectrons, smuons, and staus with a lifetime of 0.3 ns for masses up to 740, 830, and 440 GeV, respectively. Dark charginos with masses up to 380 GeV are excluded for a mass difference with the neutral state of 40 GeV, and mass differences down to 17 GeV are excluded for dark charginos with a 100 GeV mass.

supersymmetric models↗

NASA NTRS1972

Pitot-probe displacement in a supersonic turbulent boundary layer

Eight circular pitot probes ranging in size from 2 to 70 percent of the boundary-layer thickness were tested to provide experimental probe displacement results in a two-dimensional turbulent boundary layer at a nominal free-stream Mach number of 2 and unit Reynolds number of 8 million per meter. The displacement obtained in the study was larger than that reported by previous investigators in either an incompressible turbulent boundary layer or a supersonic laminar boundary layer. The large probes indicated distorted Mach number profiles, probably due to separation. When the probes were small enough to cause no appreciable distortion, the displacement was constant over most of the boundary layer. The displacement in the near-wall region decreased to negative displacement in some cases. This near-wall region was found to extend to about one probe diameter from the test surface.

Allen, J. M.↗

NASA NTRS1976

Crack-opening displacements in center-crack, compact, and crack-line wedge-loaded specimens

The theoretical crack-opening displacements for center-crack, compact, and crack-line wedge-loaded specimens (reported in the ASTM Proposed Recommended Practice for R-Curve Determination (1974)) disagree with experimental measurements in the literature. The disagreement is a result of using approximate specimen configurations and load representation to obtain the theoretical displacements. An improved method of boundary collocation is presented which was used to obtain the theoretical displacements in these three specimen types; the actual specimen configurations and more accurate load representation were used. In the analysis of crack-opening displacements in the compact and crack-line wedge-loaded specimens, the effects of the pin-loaded holes were also included. The theoretical calculations agree with the experimental measurements reported in the literature. Also examined are accurate polynomial expressions for crack-opening displacements in both compact and crack-line wedge-loaded specimens.

Newman, J. C., Jr.↗

NASA NTRS1989

Thickening oscillation of a delta wing using Navier-Stokes and Navier-displacement equations

The problem of unsteady, supersonic, locally conical, vortical flow around a delta wing undergoing thickening oscillation is solved using the unsteady, thin-layer Navier-Stokes equations and the unsteady linearized Navier-displacement equations. The unsteady, thin-layer Navier-Stokes equations are solved using the implicit approximate-factorization finite-volume scheme to compute the conservative components of the flow vector field. With the conservative components known at any time step, the linearized, Navier-displacement equations are solved using the alternating, direction-implicit scheme to obtain the grid points displacements due to known displacement boundary conditions. A grid-displacements limiter, in the form of a low mesh Reynolds number, is used to limit grid-folding in regions of highly reversed flow.

Chuang, Hsin-Kung A.↗

NASA NTRS1993

A displacement gradient BEM for accurate stress computation near boundaries in 2-D anisotropic problems

A displacement gradient method for 2D anisotropic elasticity problems is presented, which effectively minimizes the boundary layer effect through a two-step procedure. First, the boundary integral equations are solved for the unknown boundary displacements and tractions. Second, a direct integral equation for displacement gradients is developed in terms of boundary tractions. Three methods based on different evaluation procedures and locations for determining the displacement gradients are proposed. In the first method the displacement gradients are averaged at nodes common to adjacent elements. The second method stores the gradients element-wise. In the third method, the gradients are evaluated at the nodes of discontinuous elements. The three methods are applied to near-isotropic plates with circular and elliptic cutouts. It is concluded that all three methods can yield accurate stress distributions.

Sistla, R.↗