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Showing papers on "Deflection (engineering) published in 1983"


Journal ArticleDOI
TL;DR: In this article, a fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles, based on a determination of the initial tilt and the maximum twist of the crack front between particles.

1,287 citations


Journal ArticleDOI
TL;DR: In this article, particle morphology and size were examined with respect to toughening by crack deflection in a series of hot-pressed silicon nitrides comprised of rod-shaped grains of various aspect ratios and a barium-alumino-silicate glass ceramic containing spherulites.

466 citations


Journal ArticleDOI
TL;DR: In this paper, a stochastic finite element analysis method was developed for solving a variety of engineering mechanics problems in which physical properties exhibit one-dimensional spatial random variation, illustrated by evaluating the second-order statistics of the deflection of a beam whose rigidity varies randomly along its axis.
Abstract: A method of stochastic finite element analysis is developed for solving a variety of engineering mechanics problems in which physical properties exhibit one-dimensional spatial random variation. The method is illustrated by evaluating the second-order statistics of the deflection of a beam whose rigidity varies randomly along its axis. A key component of the approach is a new treatment of the correlation structure of the random material property in terms of the variance function and its principal parameter, the scale of fluctuation. The methodology permits efficient evaluation of the matrix of covariances between local spatial averages associated with pairs of finite elements. Numerical results are presented for a cantilever beam, with deformation controlled by shear, subjected to a concentrated force at its free end or to a uniformly distributed load.

417 citations


Journal ArticleDOI
Subra Suresh1
TL;DR: In this paper, a simple elastic deflection model is developed to estimate the growth rates of nonlinear fatigue cracks subjected to various degrees of deflection, by incorporating changes in the effective driving force and in the apparent propagation rates.
Abstract: The influences of crack deflection on the growth rates ofnominally Mode I fatigue cracks are examined. Previous theoretical analyses of stress intensity solutions for kinked elastic cracks are reviewed. Simple elastic deflection models are developed to estimate the growth rates of nonlinear fatigue cracks subjected to various degrees of deflection, by incorporating changes in the effective driving force and in the apparent propagation rates. Experimental data are presented for intermediate-quenched and step-quenched conditions of Fe/2Si/0.1C ferrite-martensite dual phase steel, where variations in crack morphology alone influence considerably the fatigue crack propagation rates and threshold stress intensity range values. Such results are found to be in good quantitative agreement with the deflection model predictions of propagation rates for nonlinear cracks. Experimental information on crack deflection, induced by variable amplitude loading, is also provided for 2020-T651 aluminum alloy. It is demonstrated with the aid of elastic analyses and experiments that crack deflection models offer a physically-appealing rationale for the apparently slower growth rates of long fatigue cracks subjected to constant and variable amplitude loading and for the apparent deceleration and/or arrest of short cracks. The changes in the propagation rates of deflected fatigue cracks are discussed in terms of thelocal mode of crack advance, microstructure, effective driving force, growth mechanisms, mean stress, slip characteristics, and crack closure.

331 citations


Journal ArticleDOI
TL;DR: In this article, the dependences of maximum free standing length and beam deflection on the thickness of a polycrystalline silicon beam were investigated, and annealing the poly-Si prior to beam formation was improved.
Abstract: Using the conventional MOS planar process, miniature cantilever and doubly supported mechanical beams are fabricated from polycrystalline silicon. Poly‐Si micromechanical beams having thicknesses of 230 nm to 2.3 μm and separated by 550 nm to 3.5μm from the substrate are made in a wide range of lengths and widths. Two static mechanical properties are investigated: the dependences of maximum free‐standing length and beam deflection on the thickness of the beam. By annealing the poly‐Si prior to beam formation, both of these properties are improved. Nonuniform internal stress in the poly‐Si is apparently responsible for the beam deflection.

206 citations


Journal ArticleDOI
J. N. Reddy1
TL;DR: In this article, a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense) was used to calculate frequencies, static response and dynamic response under applied loads.
Abstract: Forced motions of laminated composite plates are investigated using a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense). The present results when specialized for isotropic plates are found to be in good agreement with those available in the literature. Numerical results of the nonlinear analysis of composite plates are presented showing the effects of plate thickness, lamination scheme, boundary conditions, and loading on the deflections and stresses. The new results for composite plates should serve as bench marks for future investigations. mation are assumed to remain straight and normal to the midsurface after deformation (i.e., transverse shear strains are zero), has been used to calculate frequencies, static response, and dynamic response under applied loads. Recent studies in the analysis of plates have shown that the effect of the transverse shear strains on the static and dynamic response of plates is significant. For example, the natural frequencies of vibration predicted by the classical plate theory are 25% higher, for plate side-to-thickness ratio of 10, than those predicted by a shear deformation theory (SDT). In transient analysis of plates the classical plate theory predicts unrealistically large phase velocities in the plate for shorter wavelengths. The Timoshenko beam theory,3 which includes transverse shear and rotary inertia effects, has been extended to isotropic plates by Reissner 4'5 and Mindlin,6 and to laminated anisotropic plates by Yang et al.7 A generalization of the von Karman nonlinear plate theory for isotropic plates to include the effects of transverse shear and rotary inertia in the theory of orthotropic plates is due to Medwadawski,8 and that for anisotropic plates is due to Ebcioglu.9 With the increased application of advanced fiber composite material to jet engine fan or compressor blades, and in high performance aircraft, studies involving transient response of plates made of such materials are needed to assess the capability of these materials to withstand the forces of impact due to foreign objects (e.g., the ingestion of stones, nuts and bolts, hailstones, or birds in jet engines). Previous in- vestigations into the linear transient analysis of composite plates include Moon's10'11 investigation of the response of infinite laminated plates subjected to transverse impact loads at the center of the plate; Chow's12 study of laminated plates (with transverse shear and rotary inertia) using the Laplace transform technique; the Wang et al. 13 investigation, by the method of characteristi cs, of unsymmetrical orthotropic laminated plates; and Sun and Whitney's14'15 study of plates under cylindrical bending. More recently, the present author16'17 investigated the linear transient response of layered anisotropic composite rectangular plates and presented extensive numerical results for center deflection and stresses.

166 citations



Journal ArticleDOI
TL;DR: Theoretical analyses for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration, are presented in this paper.
Abstract: Theoretical analyses are presented for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration The dynamic analog of the Marguerre equations is used and the steady-state solutions are obtained by first applying the Galerkin method and then the harmonic balance method Actual calculations are carried out for the square plate under the assumption of the three degrees-of-freedom system and the frequency response characteristics and typical waveforms are determined under various initial edge displacements including initially buckled cases Effects of both initial deflection and initial edge displacement on the static deflection as well as the lower natural frequencies are also clarified

58 citations



Journal ArticleDOI
TL;DR: A technique for altering the grating frequency by changing the wavelength of the control beams and the use of a novel optical system to maintain the Bragg condition over a wide range of frequencies is reported on.
Abstract: Light deflection is accomplished by diffraction from a transient index modulation established as a grating of variable frequency in an optical material by the interference of two controlling light beams. This device may be considered an opto-optical analog to an acoustooptical deflector, in that a change in angular deflection is created by altering the frequency of the diffraction grating. In this paper we report on a technique for altering the grating frequency by changing the wavelength of the control beams and the use of a novel optical system to maintain the Bragg condition over a wide range of frequencies. Configurations exhibiting very large angular deflections have been designed using a computer simulation and optimization program that allows minimization of the Bragg detuning. This new method of light deflection allows either discrete or continuous light scanning or modulation. A particular example using lithium niobate will be discussed which produces an 11.8° deflection from a 0.027-μm wavelength change and with an angular detuning of less than ±0.03°. The use of other materials, inorganic, organic, and dispersive, will also be discussed.

46 citations


Patent
24 Jan 1983
TL;DR: In this paper, a banded radial run-flat tire with a dual-modulus of bending deflection behavior is described, and various types of dualmodulus behavior are obtained either by mechanical structural or by internal geometry means.
Abstract: A banded radial run-flat tire having a band with a dual-modulus of bending deflection behavior. Bands producing various basic dual-modulus characteristics are disclosed. In one type, the band has a greater resistance to bending forces tending to decrease its local radius of curvature than to those tending to flatten it. In a second type, bending stiffness increases with increasing stress irrespective of the bending direction. In a third type, a two-step modulus is demonstrated in which deflection is initially resisted at one rate and final deflection is resisted at a higher rate. Various embodiments of the band are disclosed in which the various types of dual-modulus behavior are obtained either by mechanical structural means or by internal geometry means.

PatentDOI
TL;DR: In this article, a unitary body of elastomer of the mount effects compressive deflection and bi-direction bulging of a first ring-like portion of the body, and shear of deflection of a second, tubular portion of body.
Abstract: Axial loads and motions upon a unitary body of elastomer of the mount effects compressive deflection and bi-direction bulging of a first ring-like portion of the body, and shear of deflection of a second, tubular portion of the body. The second portion of the body also imparts lateral stability to the mount. The mount can be economically manufactured and installed.

Journal ArticleDOI
TL;DR: In this article, a simple finite-element formulation for the study of postbuckling behaviour of orthotropic circular plates is presented in detail, in the form of radial load ratios along with their corresponding empirical formulae in terms of central deflection to thickness ratios of the plates.

Journal ArticleDOI
J. N. Reddy1, W.C. Chao1
TL;DR: In this article, finite element results for geometrically nonlinear bending of fiber-reinforced, single-layer and two-layer cross-ply rectangular plates constructed of materials which have linear elastic properties in tension and compression that are different.

Patent
16 Jun 1983
TL;DR: In this paper, a multirange, variable capacitance pressure transducer provided by bonding a diaphragm plate that is conductive between a pair of insulating plates is described.
Abstract: A multirange, variable capacitance pressure transducer provided by bonding a diaphragm plate (18) that is conductive between a pair of insulating plates (10,16). The diaphragm plate has a plurality of cavities provided on each side so that diaphragm deflection areas of different sizes are defined. The surfaces of the pair of plates in the cavities are covered by a conductive coating (24,26,28,30) so that the coatings form capacitors with the deflection areas. A fluid communication path is provided to each cavity so that the pressure difference to be measured is placed across the deflection area. Electrical connection is made to selective combinations of said capacitors to provide pressure transducers for a number of ranges in one unit.

Patent
29 Dec 1983
TL;DR: In this article, a flexible strip divides a shoe sole into toe and instep sections, and the toe deflection means lifting the toe section when the shoe is in a weighted state.
Abstract: A flexible strip divides a shoe sole into toe and instep sections Toe deflection means lifts the toe section when the shoe is in a weighted state Toe deflection means includes a toe plate coupled to the toe section of the sole and an instep plate coupled to the instep section of the sole The toe deflection means pivots the toe section of the sole about the flexible strip by applying bending forces to the toe and instep sections of the sole

Journal ArticleDOI
TL;DR: In this paper, the behavior of eight-ply, quasi-isotropic, graphite epoxy laminates subjected to low velocity transverse impact loading was discussed and large deflection theory of plates was used to predict the load-deflection characteristics during the impact event.
Abstract: This work discusses the behavior of eight-ply, quasi-isotropic, graphite epoxy laminates subjected to low velocity transverse impact loading Large deflection theory of plates was used to predict the load-deflection characteristics during the impact event The impact model considered that the indentation, flexural and shear stiffnesses could be represented by three-equivalent springs in series The analysis of static and dynamic impact loading test-data concluded that the membrane parameter, beta, used in flexural stiffness relation was proportional to the square of the coefficient of restitution, e, of the impactor Use of beta=0443 e-squared was made in load-deflection relations to consider the drop in plate stiffness due to delamination The results of impact tests up to impact velocity 53 m/sec were found in close agreement with the predictions

Journal ArticleDOI
TL;DR: By means of the perturbation method, a solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center is presented in this paper, where a load distribution function is introduced so as to make the compound loads depend on a single load parameter.
Abstract: By means of the perturbation method, this paper presents an approximate solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center. The special case of vanishing central deflection is also discussed. In this paper, a load distribution function is introduced so as to make the compound loads depend on a single load parameter, and average angular deflection is used as the single displacement perturbation parameter.

Journal ArticleDOI
TL;DR: In this article, the Fourier coefficients in the expansions representing the transverse deflection and rotations of normals to the plate midsurface are analyzed for both Mindlin's plate theory and a new plate theory, which allows for warping of transverse sections of the plate.

Journal ArticleDOI
TL;DR: In this article, a simple formula for the maximum bending moment and shearing force in the deck due to concentrated and distributed loads is given for suspension bridges with flexible decks, and a graph of maximum gravity stiffness deflections and changes of slope due to distributed loads are presented.
Abstract: Although classical suspension bridges have been designed for over 70 years using the deflection theory, it is difficult to obtain from literature a clear understanding of their structural action. The all‐important “gravity stiffness” is isolated from the modifying effects due to cable extensibility, tower stiffness, and deck bending stiffness. Graphs of maximum gravity stiffness deflections and changes of slope due to concentrated and distributed loads are presented, and formula for the modifying effects are given. It is found that with flexible decks simple formula exist for the maximum bending moment and shearing force in the deck due to concentrated and distributed loads.

Journal ArticleDOI
TL;DR: In this article, two different thin-walled closed sections, one square and one rectangular, were tested in biaxial bending using displacement controlled cantilever bending tests.

Journal ArticleDOI
TL;DR: In this paper, a beam is constructed from nonlinear elastic material, and subjected to several transverse concentrated loads, and the exact expression of the curvature of the deflected shape is used in the Bernoulli-Euler relationship.
Abstract: Thin beams, being flexible, form a curve with large deflections when subjected to sufficiently large transverse loads. Therefore, geometrical nonlinearity occurs, and the problem must be formulated in terms of the nonlinear theory of bending. In this paper, the beam is constructed from nonlinear elastic material, and subjected to several transverse concentrated loads. Due to the large deflection of the beam, the exact expression of the curvature of the deflected shape is used in the Bernoulli-Euler relationship. Therefore, this leads to a second order nonlinear differential equation for the transverse deflection. The solution of this equation is obtained by using the fourth-order Runge-Kutta method, and the arc length is evaluated using Simpson's Rule. The results obtained from this procedure are compared with previously published results for thin beams of linear elastic materials in order to verify the theory and the method of analysis.

Patent
08 Jul 1983
TL;DR: A torque readout sensor for mounting to a bolted interconnection between an aircraft brake assembly and a brake reaction torque limiting apparatus to sense the reaction torque upon the application of braking action is described in this article.
Abstract: A torque readout sensor for mounting to a bolted interconnection between an aircraft brake assembly (26) and a brake reaction torque limiting apparatus (30) to sense the reaction torque upon the application of braking action comprises a metal body (100,120,130,150) that replaces a bushing (54) at the bolted interconnection and configured such that a deflection of the body is accomplished in the direction of the reaction torque force and at least one pair of strain gauges (112,126,136,156) are affixed to the body at the point of deflection to provide an output electrical signal calibrated to the amount of deflection and thus to the reaction torque experienced by the body.

Journal ArticleDOI
TL;DR: In this article, the effect of web distortion on the lateral buckling of I-beams whose top flanges are unrestrained at seat supports is studied by using a finite element method.
Abstract: The effect of web distortion on the lateral buckling of I-beams whose top flanges are unrestrained at seat supports is studied by using a finite element method. The theoretical predictions are shown to agree well with available experimental results. The results of the study are used to evaluate present design code approximations, which are found to be unconservative for short length beams, and over-safe for long length beams. An improved approximation is suggested for beams in uniform bending which buckle in a symmetric mode.

Journal ArticleDOI
TL;DR: In this article, the behavior of fabricated tubular steel beam-columns as commonly used in offshore structures is studied for the entire range of monotonic loading up to ultimate load including the postbuckling branch of unloading, using assumed deflection method.
Abstract: Behavior of fabricated tubular steel beam-columns as commonly used in offshore structures is studied for the entire range of monotonic loading up to ultimate load including the post-buckling branch of unloading, using assumed deflection method. In the present approach, equilibrium is established only at a critical section of a beam-column using closed form analytical expressions for moment-curvature-thrust relationship of a fabricated tube. The computer model developed on the basis of this approximation is compared with tests and other analytical methods, and it is found that the assumed deflection method predicts the behavior of actual tubes with good accuracy, yet it simplifies the analysis drastically. A considerable amount of data has been obtained and presented concerning the behavior of cylindrical tubular beam-columns. It is concluded from this numerical study that initial imperfection (out-of-straightness), lateral load at mid-span, and bending moment at ends affect the behavior of a beam-column in a similar manner. As these values increase, the ultimate strength is reduced significantly while their associated load-deflection or shortening relations become flatter.

Journal ArticleDOI
TL;DR: In this paper, the postbuckling behavior of a simply supported rectangular thick plate subjected to arbitrary loading conditions is investigated and the applied stress is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate.
Abstract: The postbuckling behavior of a simply supported rectangular thick plate subjected to arbitrary loading conditions is investigated. The applied stress is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate. Governing equations based on von Karman assumptions are used to solve the postbuckling problem by the Galerkin method. Buckling loads are obtained to compare with the results of Brunelle and Robertson. Postbuckled deflection is shown to increase with the transverse isotropic coefficient 5, and the effects of the in-plane bending stress are found to be quite significant for a thick plate.

Journal ArticleDOI
TL;DR: In this paper, the authors compared the deflection of wooden beams loaded repeatedly for seven or two days in every 14 were compared with those of beams under constant load over a period of six months in a constant environment.
Abstract: SummaryDeflections of wooden beams loaded repeatedly for seven or two days in every 14 were compared with those of beams under constant load over a period of six months in a constant environment. Four load levels were applied to beams of three species. Loads ranged from 17 to 67 per cent of short-time failing load estimated from matched specimens. The deflections under intermittent loads were lower than the creep deflections under constant load and, with the exception of material under high stress, applicability of Boltzmann's principle of superposition of deformations was confirmed. Non-linearity at high stresses is linked with other signs of weakening after application of loads in excess of about 50 per cent of short-time ultimate.

01 Jan 1983
TL;DR: In this article, a comparison between two different methods of determining the stiffness of a motorcycle frame is made, one employing conventional, static loading of the frame with deflections and mode shape measured by dial gauges.
Abstract: A comparison between two different methods of determining the stiffness of a motorcycle frame is made. The first employs conventional, static loading of the frame with deflections and mode shape measured by dial gauges. The second entails dynamic loading of the frame by means of a sinusoidally driven shaker with deflections obtained by means of an accelerometer, electronic data processing then yielding frequency response information. Conclusions are drawn about the implications for accurate modelling of motorcycle steering behaviour arising from differences between the static and dynamic properties of the frame.

Patent
19 Apr 1983
TL;DR: In this article, an electric pickup is used to adjust the angle of articulation of a safety belt in contact with the shoulder of the occupant to a predetermined value with the aid of a comparison circuit.
Abstract: An adjusting device for the point of articulation or the point of deflection of a safety belt in automotive vehicles permits continuous adjustment of the angle of articulation for the safety belt in contact with the shoulder of the vehicle occupant to a predetermined value with the aid of an electric pickup for the angle of articulation, arranged at the point of articulation or deflection, and a comparison circuit connected after this pickup, which comparison circuit contains the predetermined value.

Patent
14 Mar 1983
TL;DR: In this article, the phase difference due to deflection of the blade tip can be used to give a measure of the deflection, and that can be displayed graphically as shown in FIGS. 7-10 for the various blades at various speeds.
Abstract: In a method of detecting the deflection of the blades 13 of a helicopter rotor as it rotates, a beam 14 of radiation from a transmitter/receiver 11 encounters the tips of the rotating blades which send reflected signals to the receiver. The phase difference due to deflection of the blade tip can be used to give a measure of the deflection of each blade, and that can be displayed graphically as shown in FIGS. 7-10 for the various blades at various speeds. In a related method of measuring deflections of the blades 111 for a tail rotor, a laser beam transmitter 16 in FIG. 14 has its reflected beam 122, 123 from an undeflected blade 111 or a deflected blade 111' received by a particular receiver in a linear array 119 of receivers so that the particular receiver gives an indication of the amount of deflection.