Showing papers on "Displacement (vector) published in 1979"

Large displacement analysis of three‐dimensional beam structures

Abstract: An updated Lagrangian and a total Lagrangian formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.

On the Euler-Lagrange transformation and the stokes' drift in the presence of oscillatory and residual currents

Abstract: It is shown that in an Eulerian velocity field consisting of a spatially varying component on which a uniform oscillatory component is superimposed, the residual mass transport velocity at a certain place is in general different from the residual Lagrangian velocity of a parcel labeled at that place. The approximation of the rigorous Euler-Lagrange transformation leading to the familiar derivation of the Stokes' drift is examined. The latter is a two-fold truncation of expansions of the former in a series of equations and a Taylor series of derivatives. The truncation of the latter series breaks down in cases of considerable spatial variability of the current velocity field, whereas the truncation of the former series may still be used if the uniform current velocity component energetically dominates the spatially varying component. It is then shown that the error introduced by substituting the local mass transport velocity for the residual Lagrangean velocity depends on the ratio of the amplitude of horizontal displacement, due to the uniform oscillatory component, to the integral length scale of the spatially varying component of the velocity field. Errors are largest if this ratio is of order 1. Such a situation may occur particularly in shallow tidal areas of complicated geometry.

An optimization procedure for stress concentrations by the finite element technique

Abstract: Load-free notch surfaces of bodies made of a linear-elastic, homogeneous, isotropic material are optimized within given variation domains by means of an interation procedure so that the occurring maximum tangential stress is reduced to a minimum. The hypothesis of a constant tangential stress distribution for obtaining minimal notch stresses proposed by R. V. Baud has been confirmed by means of the Fade-away Law of the notch stress theory. The finite element method is applied for calculating the displacement and stress field of the styructure. An increment procedure is used for determing the displacement field after every iteration step, which permits the calculation of the displacement quantities with sufficient accuracy in a single step. Numerical solutions and their comparison with analytical solutions and stress results obtained with the aid of photo-elasticity confirm the usefulness of this procedure. The known optimization methods1,2 differ from those used in the present paper.

A simple flat triangular shell element revisited

Abstract: The 18 degree-of-freedom flat triangular shell element is reformulated by combining the well-known bending triangle with a plane stress triangle incorporating in-plane rotations at each vertex. Both elements are displacement formulated. The plane stress element's displacement interpolation is incomplete and hence convergence to exact solutions is precluded. Comprehensive test results are presented for several types of problem including plane stress, thin shells and folded plates. The results indicate that the element does produce rapidly convergent answers. However these answers are not the correct ones, although they may be acceptable engineering approximations in many applications. Further, the element seems to provide reasonably good results even for relatively coarse element grids.

Viscoelastic Relaxation of Cyclic Displacements on the San Andreas Fault

Abstract: It is recognized that displacements on major plate margin faults such as the San Andreas Fault in California occur episodically. In this paper we construct a mathematical model of the fault as the boundary between two semi-infinite lithosphere plates of finite thickness, moving in opposite directions parallel to their common boundary with constant velocities at infinity but locked together on the boundary except during great earthquakes. The surface plates behave elastically but the underlying asthenosphere, although elastic in the short term, behaves as a viscous fluid on geological time scales and is treated as a viscoelastic half space linked to the lithosphere by continuity of stress and displacement. An analytic solution is obtained for the anti-plane displacement and shear stress on the surface in terms of the displacement on the fault. We apply the solution to compute the response to an infinite sequence of stepwise offsets on the fault, and to periodic displacements. The interaction of the plates with the asthenosphere damps out the time-dependence at large distances from the plate boundary, the relaxation process being characterized by a time scale T = η/G ( η = Newtonian viscosity, G = shear modulus). The results should be applicable to understanding the time dependence of the strain as a function of distance from the San Andreas Fault.

General, Closed-Form Expressions for Acoustic Waves in Cubic Crystals

Abstract: The Christoffel elastic equations are solved for long-wavelength elastic waves of arbitrary direction in cubic crystals, and exact explicit closed expressions are obtained for the phase and group velocities and displacement amplitudes. The velocity expressions that hold in the special directions are shown to follow from the general result. The problem of determining the elastic constants from the phase velocities in a general crystallographic direction is discussed with particular reference to Brillouin scattering.

Transform domain motion estimation

Abstract: This paper introduces an algorithm for estimating the displacement of moving objects in a television scene from spatial transform coefficients of successive frames. The algorithm works recursively in such a way that the displacement estimates are updated from coefficient to coefficient. A promising application of this algorithm is in motion-compensated interframe hybrid transform- dpcm image coding. We give a statistical analysis of the transform domain displacement estimation algorithm and prove its convergence under certain realistic conditions. An analytical derivation is presented that gives sufficient conditions for the rate of convergence of the algorithm to be independent of the transform type. This result is supported by a number of simulation examples using Hadamard, Haar, and Slant transforms. We also describe an extension of the algorithm that adaptively updates displacement estimation according to the local features of the moving objects. Simulation results demonstrate that the adaptive displacement estimation algorithm has good convergence properties in estimating displacement even for very noisy images.

Elastk‐plastic dynamic analysis of structures using known elastic solutions

Abstract: A numerical method is shown to analyse the dynamic elastic-plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained. This method is applied to simply supported beams with bilinear stress-strain relations with different strain-hardening rates and to a simply supported elastic-ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method.

Magnetoresistive displacement sensor and signal reprocessing circuits therefor

Abstract: A magnetoresistive displacement sensing transducer employs a plurality of sensing elements consisting of magnetically biased magnetoresistive stripes. Each sensing element is operative to produce a signal in response to linear or rotational displacement with respect to a magnetic grating. The phases of the signals from the plurality of sensing elements are relatively displaced to permit determining direction of displacement and to increase accuracy through interpolation. A signal processing circuit uses the signals from the sensing elements and optionally their sums and differences to drive a reversible counter which is thereby updated to retain a value corresponding to the position of the transducer or the magnetic grating.

Pattern generation display system

Abstract: A pattern generation display system has a pattern code processing means, a refresh memory, a pattern generator and a pattern data processor. A pattern position on the raster scan display is defined by a base position datum and a displacement datum. The pattern code processor can calculate both of the position data as the address data for an effective operation. The refresh memory stores the code of a pattern and the displacement datum thereof at the address corresponding to the base position datum thereof. The pattern data processor completes the display of the pattern at the position deviated from the base position by the displacement datum. Such a system can easily shift the pattern generated by the pattern generator on the display screen by a small pitch. Therefore, it is easy to adjust the position of characters corresponding to the character or sentence features.

Electronic constant speed control for a hydrostatic transmission

Abstract: An electronic constant speed control for a hydrostatic transmission having a variable displacement hydraulic pump with a displacement controlling member movable to various positions at either side of a neutral position and having an input shaft connectable to a prime mover and a hydraulic motor having an output shaft, an electric controller for positioning siad displacement controlling member, a command potentiometer for establishing a set constant speed signal representing a desired constant speed between zero and maximum speed in either direction of rotation for said output shaft, a speed detecting device for establishing a pump input shaft speed signal, a circuit for generating a position control signal representing the required position of the displacement controlling member for the set speed which is responsive to the constant speed and pump input shaft speed signals, a speed detecting device for establishing an output shaft speed signal, a circuit for comparing the output shaft speed signal with said set constant speed signal and integrating any error therebetween and generating a speed error control signal, and a summing circuit for summing said position and speed error control signals to provide a control signal to said electric controller.

Profile control system

Abstract: A difference signal corresponding to the difference between the displacement of a stylus of a tracer head and a reference signal is integrated and the sum of the integrated value and the difference signal is applied as an error signal to a command velocity function generator and a correcting velocity function generator to produce a command velocity signal and a correcting velocity signal, respectively, which are provided to a distributing circuit. A displacement direction signal from an index circuit is supplied to the distributing circuit to derive therefrom respective axis command velocity signals for effecting profile control.

Visual cue simulator

Abstract: A simulator arrangement wherein visual cues are generated by a video system at a display surface (18) spaced from an eye position (14). The image at the display surface is formed as longitudinal boundaries emanating from a vanishing point (VP) positioned a predetermined distance above a fixed horizon (30) image. Hue and texture visual information are developed between the longitudinal boundaries from a memory function (178). The slopes of the longitudinal boundaries are developed as the quotient of the value of the transverse displacement of a boundary from the corresponding position of the eye position divided by a value representing simulated height of the eye position. The arrangement finds particular utilization in conjunction with flight trainers.

Servo control system operable on digital basis with limit cycle suppressed

Abstract: In a digital servo control system (31) for a carriage of a serial printer or a like movable element, a control signal (125) digitally represents a reference angular velocity for a motor (26) until an instant at which a displacement from a current position of the element to a commanded position decreases to a predetermined value, a positional error during a preselected interval following the instant, and an integrated value (52) of a position error between the current and the commanded positions to suppress limit cycle after the interval. A PWM signal (56-57) is derived from the control signal and position pulses (62 or 63) representative of a variation in the current position. Preferably, small-amplitude limit cycle is forced to occur during the interval with the positional error indicated by a modified signal (182) derived by adding unity to positive and zero position errors.

Digital position transducer including variable tuning element oscillator

Abstract: A digital position transducer apparatus utilizing a moveable slug-tuned inductor to measure the displacement or movement of a mechanical component. The value of the inductor controls an oscillator's output frequency which is converted to a digital word proportional to the displacement of a mechanical component.

Computer Program for Calculation of Separated Turbulent Flows on Axisymmetric Afterbodies including Exhaust Plume Effects

Abstract: : A computer code for a turbulent boundary-layer, inviscid interaction method for axisymmetric configurations of the type used for isolated nozzle afterbody models is presented. The method is applicable to flows with subsonic free streams, including slightly supercritical flows and to bodies with either high pressure exhaust plumes or solid plume simulators. The method consists of an integral boundary-layer and plume-entrainment method and a finite-difference inviscid-flow method which are coupled iteratively through the boundary-layer displacement thickness. Both attached and separated boundary layers can be calculated. An option is provided for calculating two-dimensional boundary layers. The procedure for separated flows is to specify the displacement thickness of the boundary layer and calculate the free-stream velocity distribution from both the boundary-layer equations and the inviscid-flow equations. The separation point location and the angle of the displacement surface are found by an iterative procedure.

The construction of displacement fields of dislocation loops and stacking-fault tetrahedra from angular dislocation segments

Abstract: The computer simulation of electron microscope images of lattice defects requires detailed knowledge of the displacement fields of the defects. By using the method of Yoffe (1960), expressions are derived for the displacement field of a regular N -sided polygonal dislocation loop of arbitrary Burgers vector, and of a stacking-fault tetrahedron, in forms suitable for use in image simulation.

Spline function approximation in discrete mechanics

Abstract: It is shown that the fundamental equations in discrete mechanics are consistency relations for a parametric spline function approximation. The formula which relates displacement and acceleration is of O((Δt)2 and unconditionally stable in the sense of Dahlquist. This method is equivalent to two first order difference equations which relate velocity and acceleration, and displacement and velocity.

Position Sensors And Actuators For Figure Control Of A Segmented Mirror Telescope

Abstract: A control system using mirror displacement sensors and position actuators to maintain proper surface control of a segmented mirror is summarized. The system is composed of three major components; a figure control computer, displacement sensors and displacement actuators. Desired positioning accuracy is 50 nm. Several methods for achieving the needed sensor sensitivity and stability are discussed. A capacitive hridge detector was chosen and its expected and measured behavior is described. Two mechanisms for positioning a mirror segment to optical tolerances, yet having a large dynamic range to compensate for mirror cell deformation are reviewed. Test results for a roller screw are given with an outline of the servo loop design.

Method of and system for tracking an object radiating a circularly or linearly polarized electromagnetic signal

Abstract: The method for tracking an object emitting a circularly or linearly-polarized electromagnetic wave utilizes only the TE21 mode signals, extracted by means of two pairs of slots (A, A'; B, B') located on planes at π/4 in the antenna feed. The signals of a slot pair are substracted one from the other and the resulting signals are made proportional to the antenna displacement from nominal object direction. This is obtained by making an angle ϕ, that determines the angular position of the plane passing through a pair, equal to half an angle a, that determines the angular position of the polarization plane. The system that carries out the method is also described.

Transducer for measuring workpieces

Abstract: A caliper-type transducer for measuring a workpiece includes a pair of non-crossing pivot arms each having a contact end and a transducer end. The arms are interconnected for frictionless pivotal movement by a fixed pivot block and spring members which act to limit the displacement of the arms to complemental displacement in the plane of measurement. One arm carries two reactive elements mounted in spaced opposed relationship such that the transducer end of the other arm may be disposed therebetween to vary the reactances according to movement of the caliper ends which cause corresponding movement in their respective transducer ends. The change in reactances of the reactive elements are differentially sensed as the arms are displaced from an initial position when measuring the workpiece.

Sandwich hologram interferometry. 5: Measurement of in-plane displacement and compensation for rigid body motion.

Abstract: Sandwich holography has been used for measurements of in-plane displacement of an object. The sign of the displacement is found by tilting the sandwich hologram during reconstruction. Fringes caused by in-plane rigid body motion can be compensated for, and local displacements evaluated. It is shown that an in-plane motion of more than 1 mm of the object placed at a distance of about 1 m from the plates can be compensated for and a local tilt of 1.5 × 10−3 degrees evaluated. A comparision between conventional evaluation and evaluation of sandwich holograms by measuring the tilt angle of the plates to calculate an object’s displacement is shown with a series of experiments.