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

Stochastic finite element analysis of simple beams

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.

Crack deflection: Implications for the growth of long and short fatigue cracks

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.

Polycrystalline Silicon Micromechanical Beams

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.

Geometrically nonlinear transient analysis of laminated composite plates

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.

Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement— Part II: Experiment

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

Static and dynamic lateral deflexion of piles in non-homogeneous soil stratum

Abstract: The Paper presents the results of a systematic parametric investigation of the static and dynamic response of single free-head piles embedded in a soil stratum, the modulus of which increases linearly with depth. The study is conducted by means of a dynamic finite-element formulation which accounts for the three-dimensionality of soil deformation while properly reproducing the radiation damping characteristics of the system. The soil is modelled as a linear hysteretic continuum and the excitation consists of a sinusoidally time-varying horizontal force or moment, applied at the pile head. Comprehensive plots of the results are presented in non-dimensional form, for a wide range of the most significant dimensionless groups of problem parameters. For the response of flexible piles, in particular, simple algebraic expressions are developed in terms of the ratio E,/E,, of the pile and soil moduli. These expressions, being valid for several values of Poisson’s ratios of the soil, compare favourably with results from previous studies and are expected to be useful in practical design calculations.

Opto-optical light deflection

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.

Dual-modulus band banded tire

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.

Compact low-frequency engine mounting

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.

Transverse Shear Effects in Bimodular Composite Laminates

Abstract: A closed-form solution for the Timoshenko-type shear correction coefficient (K2) governing the deflection of bimodular composite laminates in cylindrical bending is presented. The bending- stress distribution for a laminate constructed of bimodular materials (which have different elastic moduli in tension and compression) is used in the two-dimensional equilibrium equation to obtain the transverse shear-stress distribution. This shear-stress distribution is used to obtain expressions for the shear correction coefficient (based on equrvalent shear strain energy) and the maximum dimensionless transverse shear stress (τxz) max. Finally, the effects of the elastic-constant ratios on the neutral-surface location and shear correction coefficient for laminates consisting of either unimodular or bimodular materials are studied.

Multiple range capacitive pressure transducer

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.

Toe lifting shoe

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

Low velocity transverse impact behavior of 8-ply, graphite-epoxy laminates

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

Residual Strength Assessment of Low Velocity Impact Damage of Graphite-Epoxy Laminates

Abstract: This report contains the study of Low Velocity Transverse Impact Damage of graphite-epoxy T300/5208 composite laminates. The specimen, 100 mm diameter clamped plates, were impact damaged by a cantilever-type instrumented 1-inch diameter steel ball. Study was limited to impact velocity 6 m/sec. Rectangular strips, 50 mm x 125 mm, were cut from the impact-damage specimens so that the impact damage zone was in the center of the strips. These strips were tested in tension to obtain their residual strength. An energy dissipation model was developed to predict the residual strength from fracture mechanics concepts. Net energy absorbed I(a) was evaluated from coefficient of restitution concepts based on shear dominated theory of fiber-reinforced materials, with the modification that during loading and unloading the shear deformation are respectively elastic-plastic and elastic. Delamination energy I(d) was predicted by assuming that the stiffness of the laminate dropped due to debonding. Fiber-breakage energy, assumed to be equal to the difference of I(a) and I(d), was used to determine the residual strength. Predictions were compared with test results.

Large deflection of circular plate under compound load

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.

Domain Structure and Deflection of Light at Domain Walls in RbHSeO4

Abstract: Domain structures of feroelectric RbHSeO 4 , which undergoes phase transitions at 102°C and 173°C, were observed and examined in the presence of either electric field or shear stresses, and the intensity of a laser beam deflected at domain walls was measured. In addition, dielectric and piezoelectric examinations were made above and below the 102°C transition. It was found that there are two types of domain structures observable at room temperature, i.e., the ferroelectric and simultaneously ferroelastic domain struc-structure with the (001) domain walls and the ferroelastic one with the (100) domain walls. The former is observable below 102°C, while the latter is observable even above 102°C. The intensity of the light beam deflected at the (001) domain walls is observed to be proportional to the square of the spontaneous polarization.

Gravity stiffness of classical suspension bridges

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.

Large deflections of point loaded cantilevers with nonlinear behaviour

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.

Torque readout sensor

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.

Method of, and apparatus for, terminating a conductor of a flat flexible cable

Abstract: In a method of, and apparatus for, terminating a conductor of a flat flexible cable, a flat flexible cable is inserted into a U-shaped terminal having a resiliently deflectable arm. A camming element is then inserted into the terminal to urge the cable against a contact surface of the deflectable arm, the cable having been previously stripped of insulation on its side adjacent to the contact surface. The deflectable arm is first elastically deflected by the action of the camming element and is thereafter plastically deflected thereby. The camming element is so dimensioned, and the resistance of the flexible arm to its plastic deflection in relation to its resistance to its elastic deflection are such that, the final contact force exerted against the cable conductor is independent, for practical purposes, of the stripped thickness of the cable, such thickness not exceeding 0.4 mm.

Lateral stability of beams on seats

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.

Post-Buckling Behavior of Tubular Beam-Columns

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.