Showing papers on "Deflection (engineering) published in 1994"

Thermal and ambient-induced deflections of scanning force microscope cantilevers

Abstract: The deflection of scanning force microscope cantilevers, metal coated on one side, is significantly influenced by both thermal heating and variations in relative humidity. For constant relative humidity, the deflection of the cantilever drifts due to laser heating and eventually reaches a steady‐state value. For a thermally stabilized cantilever, the deflection varies linearly with relative humidity. Exposure to other vapors, such as mercury, changes the inherent deflection of the cantilever. Relative amounts of adsorbates on the cantilever can be estimated from shifts in the cantilever resonance frequency with picogram mass resolution. The cantilever deflection as well as changes in resonance frequency due to vapor adsorption can be used as basis for novel chemical sensors.

Lateral load analysis of single piles and drilled shafts

Abstract: The p‐y method of analysis models nonlinear behavior, and is an effective method of designing deep foundations subjected to, lateral loads Deflections and bending moments calculated using p‐y analyses have usually been found to be in good agreement with field measurements This paper describes a method of analysis, the characteristic load method (CLM) that is simpler than p‐y analyses, but that closely approximates p‐y analysis results The method uses dimensional analysis to characterize the nonlinear behavior of laterally loaded piles and drilled shafts by means of relationships among dimensionless variables The new method is simple enough for use by manual calculation, and it can also be adapted for computer use Lateral deflections and maximum bending moments calculated using CLM have been found to be in good agreement with values measured in field load tests

Friction effects in the deflection of atomic force microscope cantilevers

Abstract: The conventional deflection‐mode atomic force microscope operates by optically monitoring the slope near the end of a microcantilever in contact with the sample surface. This signal is usually interpreted as a measure of height change. Lateral forces from friction, surface geometry, or inclination of the cantilever to the surface also affect the slope due to cantilever buckling. We calculate the deflection of a hollow triangular model cantilever subject to both lateral and normal forces. The measured response of the servo circuit to an inclined, loaded cantilever is then determined. This shows (1) errors are always present in height measurements of structures on inhomogeneous surfaces; (2) the sensitivity to buckling can be reduced by repositioning the laser; (3) friction measurements can be accurately made by scanning in two directions and applying the proper calibration.

Design of piled bridge abutments on soft clay for loading from lateral soil movements

Abstract: Piles supporting bridge abutments on soft clay may be loaded laterally from horizontal soil movements generated by the approach embankment. The design of piles loaded by lateral soil movements is problematic in that existing design approaches are generally inconsistent or show poor correlation with available data. New empirical design charts are presented to allow an assessment of maximum pile bending moment and pile head deflection based on the relative soil-pile stiffness and current loading level. A new analytical approach is also developed on the basis of a simple deformation mechanism. The method accounts for the main features of the problem through an approximate representation of the embankment-soil-pile interaction, and is shown to compare favourably with centrifuge model test data. Recommendations for the design of pile groups for loading from lateral soil movements are also given. Les mouvements horizontaux du sol crees par le remblai sont susceptibles d'engendrer des contraintes laterales dans ...

Static and free vibrational analysis of beams and plates by differential quadrature method

Abstract: The new approach for application of boundary conditions in the differential quadrature (DQ) method, proposed earlier by the present authors, is extended to generalized force boundary conditions in two dimensions A variety of problems is then analyzed by theDQ method with the new approach for application of boundary conditions, such as deflections of beams and circular and rectangular plates under nonuniformly distributed loadings, deflection of a rectangular plate on a Winkler foundation, and buckling and free vibrational analyses of circular plates It is found that the present method gives good accuracy and is computationally efficient Exact solutions can be obtained by theDQ method if analytical solutions are polynomials and the method is insensitive to the spacing of grid points for the cases considered

Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models

Abstract: Buckling of initial imperfection sensitive structure — column on a non-linear elastic foundation — is investigated. A criterion based on the concept of “modal buckling load” is proposed to determine which modes should be included in the analysis when the weighted residuals method is utilized to calculate the limit load — maximum load the structure can support — for a given initial deflection. For stochastic analysis, a random field model is suggested for the uncertain initial imperfection, and Monte Carlo simulations are performed to obtain the probability density of the buckling load and the reliability of the column. Finally, a non-stochastic convex model of uncertainty is employed to describe a situation when only limited information is available on uncertain initial deflection, and the minimum buckling load is obtained for this model. The results from both the stochastic and the non-stochastic approaches are derived and critically contrasted.

Finite element simulation of pavement discontinuities and dynamic load response

Abstract: Assumption of a linear elastic system under static loading is questionable for structural response analysis of pavement-subgrade systems under dynamic nondestructive testing and moving wheel loads, especially if a deteriorated pavement is under study. Presented are the results of a parametric study using the three-dimensional finite element ABAQUS code; it investigates the effects of pavement discontinuities and dynamic analysis on the surface deflection response of a pavement-subgrade model under a standard falling-weight deflectometer (FWD) load. An optimum three-dimensional pavement subgrade model of an 18.3-m (60-ft) pavement length was established with a fixed boundary at the bottom and roller supports on the sides. ABAQUS static deflections are in good agreement with the static deflections calculated from the traditional elastic layer analysis for an uncracked pavement. The ABAQUS dynamic response using backcalculated nonlinear moduli compares reasonably with the measured FWD deflections on an asphalt pavement site. The ABAQUS special-purpose gap elements are used to simulate longitudinal and transverse cracks in the surface layer. Dynamic deflections are 17% higher for a pavement with longitudinal cracks as compared with an uncracked pavement.

An active flexible wing multi-disciplinary design optimization method

Abstract: This paper discusses Active Flexible Wing (AFW) technology and describes how it differs from conventional wing design. The benefits of AFW are briefly described. Two design procedures which aid in the design and optimization of an AFW wing are described in detail. The first procedure is for the design of an AFW control system on an existing wing. This procedure optimizes control surface positions to maximize air vehicle maneuverability, without exceeding structural limits. The second procedure is for the design of a new wing using AFW technology. This procedure simultaneously couples aerodynamic, structural, and external load designs. The process optimizes a wing structure and control surface positions for minimum weight and drag, while satisfying structural constraints. = buckling constraints = bending moment = drag of case i = hinge moment = roll moment of load case i = lift of load case i = pitching moment of load case i = roll rate = torsion moment = twist and camber variables (e.g., wing jig shape design) = structural design variables = flutter constraints = structural weight = control surface positions and air vehicle flight angle design variables = roll axis inertia = roll acceleration = stress constraints of load case i {a} = vector of rigid aerodynamic panel deflections {!} = lift vector on aerodynamic panels * Project Engineer, Advanced Aircraft Member AIAA [ A ] = aerodynamic panel lift due to alpha influence coefficient matrix [ B ] = aerodynamic to structural transformation matrix [ K ] = global stiffness matrix [ d ~ / dtk] = derivative of the global structural stiffness matrix with respect to structural design variables [ S I ] =structural flexibility matrix (in units of deflection per force) on aerodynamic model [ S A ] = structural flexibility matrix (in units of rotation per force) on aerodynamic model

Analysis of beams containing piezoelectric sensors and actuators

Abstract: A one-dimensional theory is developed for modeling the analysis of beams containing piezoelectric sensors and actuators. The equations of motion and associated boundary conditions are derived for the vibrations of piezoelectrically sensored/actuated beams. The effect of coupling between longitudinal deflection and bending deflection is investigated. For the practical applications, in accordance with the proposed beam theory, a one-dimensional finite element formulation is presented. The proposed beam theory as well as the finite element approach can easily be used in developing a formal two-dimensional theory for piezoelectrically actuated composite plates and shells or other physical systems.

Structural stiffness and Coulomb damping in compliant foil journal bearings : parametric studies

Abstract: This paper presents the results of the second part of the investigation on structural stiffness and Coulomb damping in compliant foil journal bearings. In the first part, a theoretical model was developed to calculate equivalent viscous damping coefficients and structural stiffness of a bump foil strip in a journal bearing or damper. A computer program was also developed to compute the eccentricity and attitude angle of the journal static equilibrium position as well as the deflections, displacements, reacting forces, and equivalent friction coefficient of each bump on the strip. This model and program enabled further parametric studies to be conducted in the second part of the investigation, the results of which are the subject of this paper. The design parameters studied were static eccentricity (bearing load), pad angle (load angle), sliding friction coefficients, and perturbation amplitude (dynamic load). In addition, more effective methods of achieving both Coulomb damping and optimum structural stif...

Closure of "Creep Effects in Composite Beams with Flexible Shear Connectors"

Abstract: This paper presents a method for the viscoelastic analysis of composite steel‐concrete beams with flexible shear connectors. In particular, the proposed method evaluates the effects of the connection device's deformability on the migration of the stresses from the concrete slab to the steel beam, which occurs with time as a result of creep and shrinkage of the concrete part. The mathematical formulation of this problem involves the equations of equilibrium, compatibility, and constitutive relationships, i.e., an elastic law for the steel part and an integral‐type creep law for the concrete part. Thus, the problem is governed by a coupled system of three equations, of which two are integral‐differential‐type equations. This system of equations is resolved by numerical step‐by‐step techniques. Finally, a numerical analysis is applied to show the influence of the main parameters.

A simple triangular element for thick and thin plate and shell analysis

Abstract: A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid-side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid-sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.

Deflection of a substrate induced by an anisotropic thin‐film stress

Abstract: The deflection of a substrate caused by an anisotropic stress in a thin film that is deposited on it, is studied theoretically. An exact solution of the elastic equations for the three‐dimensional cantilever problem is found. Equations for the deflection caused by anisotropic stresses due to, e.g., magnetostriction and by isotropic stresses are given. A comparison is made between these equations and the equations usually given in the literature for the determination of thin‐film stresses.

Modeling and Shape Control of Piezoelectric Actuator Embedded Elastic Plates

Abstract: Future technologies in microsensing, microactuation, active changes in shapes of aerofoils and turbine blades justify and necessitate a comprehensive study of piezo actuators for shape control of structures. Piezo materials have the property to develop strain on applying voltage and voltage on applying strain, hence, these materials are useful both as sensors and actuators. If a piezo actuator is bonded to a substrate plate, on applying voltages, the resulting strain in the actuator induces a deflection in the plate. This deflection is a function of geometry, material properties of ac tuator and substrate, layout of piezo actuators, and voltage inputs to the actuators. The objectives of this paper are: (a) to develop a mathematical model for deflection of a thin plate embedded with piezo actuators using elastic plate theory, (b) to compute plate deflection by solving the mathematical model using finite difference technique, and (c) to estimate optimal actuation voltages to match the deflection of the plat...

Dynamic response of a cracked beam subject to a moving load

Abstract: The dynamic response of a beam with a single-sided crack subject to a moving load on the opposite side is analyzed using Euler beam theory and the assumed mode method. The beam is modeled as two separate beams divided by the crack. Two different sets of admissible functions which satisfy the respective geometric boundary conditions are assumed for these two fictitious sub-beams. The rotational discontinuity at the crack is modeled by a torsional spring with an equivalent spring constant for the crack. The transverse deflection at the crack is matched by a linear spring of very large stiffness. Results of numerical simulations are presented for various combinations of constant axial velocity of the moving load and the crack size.

Synchronous sampling scanning force microscope

Abstract: The synchronous sampling scanning force microscope includes a reflective cantilever arm having a free end which is oscillated at a frequency different from the resonance frequency of the cantilever arm. The motion of the oscillating cantilever arm is measured, to generate a deflection signal indicative of the amplitude of deflection or phase shift of the cantilever arm. Selected portions of cycles of the output signal are sampled, for generating output signal data indicative of deflection of the near and far excursions of the probe. The method and apparatus permit monitoring of compliance of the surface of the specimen by multiple sampling at a rate greater than the period of oscillation of the cantilever probe of the microscope.

Schaum's Outline of Theory and Problems of Strength of Materials

Abstract: Tension and compression statically indeterminate force systems - tension and compression thin-walled pressure vessels direct shear stresses torsion shearing force and bending moment centroids, moments of inertia and products of inertia of plane areas stresses in beams elastic deflection of beams - double-integration method elastic deflection of beams - method of singularity functions statically indeterminate elastic beams special topics in elastic beam theory plastic deformation of beams columns strain energy methods combined stresses members subject to combined loadings - theories of failure.

Effects of Membrane Stresses in the Prediction of Foil Bearing Performance

Abstract: The effects of membrane stresses which result from both viscous drag and the three-dimensional structure of an incompressible journal foil bearing are discussed. The structural model includes combined bending, membrane, and elastic foundation effects. The pressure in the lubricant film is predicted using an incompressible Reynolds equation. Finite element methods are used to predict both the structural deflections and the pressures in the lubricant film. Results will demonstrate that membrane effects are significant in an elastically supported foil bearing where elastic foundation effects are normally considered to provide the primary resistance to deflection. The effects of viscous drag are small but not insignificant. Presented at the 48th Annual Meeting in Calgary, Alberta, Canada May 17–20, 1993

Measurements of the mechanical behaviour of micromachined silicon and silicon-nitride membranes for microphones, pressure sensors and gas flow meters

Abstract: This paper mainly presents the experimental determination of the small deflection behaviour of boron-implanted silicon-nitride and highly boron-doped silicon diaphragms for micromachined silicon subminiature microphones. The additional implantation of boron into silicon-nitride diaphragms reduces the intrinsic stress in the deposited amorphous films. The minimum detectable deflection, using a Mach-Zehnder interferometer, is about 0.02 nm for dynamic measurements (A-weighted filtering). The largest measurable deflection (where nonlinearities of the interferometer are negligible) is strongly influenced by the wavelength of the laser and is about 10 nm. Thus, applying this method to pressure sensors and gas flow meters, the pressure range is restricted. In order to achieve a high sensitivity of the measuring apparatus and a low detectable deflection amplitude a feedback configuration stabilizes the interferometer in the most sensitive operation points.

Large deflection of beams under moment gradient

Abstract: Two different approaches are presented for the large-deflection analysis of an inextensible elastic beam under moment gradient. One end of the beam is hinged and at a fixed distance away from this end is a frictionless support where the beam can slide freely. In the first approach, the differential equation based on elastica theory is formulated and solved by using elliptic integrals; which yield a closed-form solution. In the second approach, the governing differential equations are solved numerically by the shooting-optimization technique in which the fourth- order Runge-Kutta algorithm and an optimization algorithm are employed. Comparison studies of the results obtained from the two methods are made and the results are found to be in very good agreement.

Buckled membranes for microstructures

Abstract: Based on energy variation methods we calculated the deflection of membranes under the combined load of an external pressure and an internal lateral stress. A lateral load gives rise to buckling once a critical load is exceeded. The combination of transversal loads and lateral loads changes the properties of the membrane (and other structures) in the vicinity of the buckling load: The membrane deflects at all lateral loads and the critical load, above which two states are possible shifts. A result important for the design of microsystems, which are based on the buckling phenomenon, is the pressure required to switch the membrane from one state to the other. The theory is tested successfully with micromachined silicon/silicon-dioxide membranes.

Method and apparatus for installing a helical pier with pressurized grouting

Abstract: A method and apparatus used to increase the stiffness characteristic of soil to improve its ability to support a structures and to provide a tie-back anchoring force. The apparatus includes an anchor having helixes thereon is rotated into the ground. The helical anchor is hollow and includes multiple perforated holes along its length and about its perimeter. Once, the anchor is drilled into the ground, pressurized grout is injected therein. The grout is forced through the helical anchor and out through the perforated holes. The grout fills any voids along the sides of the anchor and stiffens the surrounding soil. Once the grout hardens, it may be used in a tie-back application or to support new and old construction or the like. The grout surrounding the anchor increases its lateral support and prevents deflection thereof.

Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison

Abstract: A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.