Showing papers on "Deflection (engineering) published in 1999"

Robust nonlinear control of a hypersonic aircraft

Abstract: For the longitudinal motion of a hypersonic aircraft containing twenty-eight inertial and aerodynamic uncertain parameters, robust flight control systems with nonlinear dynamic inversion structure are synthesized. The system robustness is characterized by the probability of instability and probabilities of violations of thirty-eight performance criteria, subjected to the variations of the uncertain system parameters. The design cost function is defined as a weighted quadratic sum of these probabilities. The control system is designed using a genetic algorithm to search a design parameter space of the nonlinear dynamic inversion structure. During the search iteration, Monte Carlo evaluation is used to estimate the system robustness and cost function. This approach explicitly takes into account the design requirements and makes full use of engineering knowledge in the design process to produce practical and efficient control systems. A4 MY, m 4 Nomenclatm-e speed of sound, ftls drag coefficient lift coefficient moment coefficient due to pitch rate moment coefficient due to angle of attack moment coefficient due to elevator deflection thrust coefficient reference length, 80 ft drag, lbf altitude, ft moment of inertia, 7 X lo6 slug-ft2 lift, lbf Mach number pitching moment, lbf-ft mass, 9375 slugs pitch rate, radis radius of the Earth, 20,903,500 ft radial distance from Earth’s center, ft reference area, 3603 ft2 thrust, lbf velocity, ft/S angle of attack, rad throttle setting flight-path angle, rad elevator deflection, rad gravitational constant, 1.39 X 1Or6 ft3/s2~ density of air, slugsIft

Strengthening Reinforced Concrete Beams Using Fiber Reinforced Polymer (FRP) Laminates

Abstract: The behavior of reinforced concrete beams strengthened with various types of fiber reinforced polymer (FRP) laminates is presented. The experimental program included strengthening and testing 24 simply supported rectangular cross section beams. Each beam was initially loaded above its cracking load. The cracked beams were strengthened with FRP laminates and then tested until complete failure. Five available strengthening systems of various types of carbon/glass fiber reinforced polymer (CFRP/GFRP) strengthening materials were used. These materials included two types of CFRP sheets, bi- and unidirectional GFRP sheets, and CFRP plates. The effects of strengthening on deflection, failure load and failure mode, strain, and beam ductility are discussed. In addition, the influence of different numbers of FRP layers, type of epoxy, and strengthening pattern on the behavior of beams was examined. The ratio of absorbed energy at failure to total energy, or energy ratio, was used as a measure of beam ductility. It is concluded that, in addition to the longitudinal layers, the fibers oriented in the vertical direction forming a U-shape around the beam cross section significantly reduce beam deflections and increase beam load carrying capacity. Furthermore, the presence of vertical and horizontal sheets, together with a proper epoxy, can lead to a doubling of the ultimate load carrying capacity of the beam. However, all the strengthened beams experienced brittle failure, mandating a higher factor of safety in design.

Structural mechanics of buried pipes

Abstract: Preliminary Ring Design Ring Deformations Soil Mechanics Pipe Mechanics Ring Stresses Ring Deflection Ring Stiffness Non-Circular Cross Sections Ring Stability Encased Flexible Pipes Rigid Pipes Minimum Soil Cover Longitudinal Mechanics Thrust Restraints Embedment Parallel Pipes and Trenches Special Sections Stress Analysis Plastic Pipes External Hydrostatistics Buried Tanks and Silos Leaks in Buried Pipes and Tanks Long-Span Structures Economics of Buried Tanks Non-Circular Linings and Coatings Risers Analysis of Buried Structures by the Finite Element Method Economics of Buried Pipes and Tanks Appendices

Quantitative material characterization by ultrasonic AFM

Abstract: In an atomic force microscope equipped with a micromachined cantilever tip, the cantilever vibration spectra in contact with the sample were found to be strongly dependent on the excitation power. However, if the excitation power is small enough, the resonance peak width decreases and the peak frequency increases to a certain limiting value. In this condition the tip-sample contact is kept linear, and satisfactory agreement between the measured and calculated frequency is obtained, assuming a constant contact stiffness; the agreement is further improved by taking into account the lateral stiffness. More quantitative information on the elasticity of the sample is obtained from the contact load dependence of the frequency, where contact stiffness of a non-spherical tip shape is derived from the Sneddon-Maugis formulation, and the tip shape index is estimated by an inverse analysis of the load-frequency relation. A further advantage of evaluating not only the vertical but also the lateral stiffness is demonstrated on a ground silicon wafer by simultaneous measurement of deflection and torsional vibration.

New Shear Actuated Smart Structure Beam Finite Element

Abstract: We present the formulation and validation of a new adaptive sandwich-beam finite element, capable of dealing with either extension or shear actuation mechanisms, which is reached by coating an elastic core with piezoelectric sheets or sandwiching a piezoelectric core between two elastic faces. The poling direction is taken parallel to the transversely applied electric field for the first mechanism and in the axial direction for the second one. The sandwich construction is made of asymmetric thin faces (Euler-Bernoulli beams) and a relatively thick core (Timoshenko beam). The obtained two-node finite element has only four mechanical degrees of freedom that are the deflection and its derivative and the mean and relative axial displacements of the faces midplanes. Finite element analysis of segmented and continuous cantilever adaptive sandwich beams with active faces (extension actuated) or core (shear actuated) show good comparisons with results found in the Iiterature, Additional parametric studies (actuator's position and thickness, structure's stiffness) with the present element indicate that the shear actuation mechanism presents several promising features over the conventional extension actuation mechanism. In fact, the shear actuation mechanism is better than the extension one for stiff structures and thick piezoelectric actuators.

Apparatus for r-f ablation

Abstract: An improved system and method for ablating a tissue site is provided. In one embodiment, the system comprises an ablation catheter employing one or more electrodes and multiple temperature sensors located along the catheter distal end. The temperature sensors control the power applied to the one or more electrodes. A deflection mechanism may be included to provide directional control to the catheter.

Deflection Calculation for Reinforced Concrete Structures—Why We Sometimes Get It Wrong

Abstract: The simplified procedures contained in the American Concrete Institute (ACI) 318 Building Code for calculating the deflection of beams and slabs are inadequate in some situations. The provisions in the current Australian Code AS 3600-1994, which are similar to those in ACI 318, have recently been found wanting in a variety of situations and are currently under review. The calculated deflection is often significantly less than the actual deflection, and serviceability problems resulting from excessive deflection are not uncommon for structures designed in accordance with the code. In this paper, the deficiencies of the existing approach are discussed and demonstrated by a comparison with experimental results. Suggestions for improving the procedure are also proposed and evaluated.

Estimated Benefits of Variable-Geometry Wing Camber Control for Transport Aircraft

Abstract: Analytical benefits of variable-camber capability on subsonic transport aircraft are explored. Using aerodynamic performance models, including drag as a function of deflection angle for control surfaces of interest, optimal performance benefits of variable camber are calculated. Results demonstrate that if all wing trailing-edge surfaces are available for optimization, drag can be significantly reduced at most points within the flight envelope. The optimization approach developed and illustrated for flight uses variable camber for optimization of aerodynamic efficiency (maximizing the lift-to-drag ratio). Most transport aircraft have significant latent capability in this area. Wing camber control that can affect performance optimization for transport aircraft includes symmetric use of ailerons and flaps. In this paper, drag characteristics for aileron and flap deflections are computed based on analytical and wind-tunnel data. All calculations based on predictions for the subject aircraft and the optimal surface deflection are obtained by simple interpolation for given conditions. An algorithm is also presented for computation of optimal surface deflection for given conditions. Benefits of variable camber for a transport configuration using a simple trailing-edge control surface system can approach more than 10 percent, especially for nonstandard flight conditions. In the cruise regime, the benefit is 1-3 percent.

Externally Prestressed Members: Evaluation of Second-Order Effects

Abstract: The deterioration of bridges due to increased traffic loading, progressive structural aging, and reinforcement corrosion from severe weathering conditions has become a major problem around the world. External prestressing is considered one of the most powerful techniques used for strengthening or rehabilitation of existing structures and has grown to occupy a significant share of the construction market. This paper presents the results of an analytical investigation of the strength and structural behavior of concrete members prestressed with external tendons. The behavior at both the serviceability and ultimate limit states is evaluated. A nonlinear analysis model, based on the incremental deformation method, is developed to predict the entire response of concrete members originally designed with or strengthened by external prestressing. The proposed analysis reproduced experimental results of deflection and tendon stress responses with remarkable accuracy. A parametric study was undertaken to evaluate the behavior of concrete beams either designed using external prestressing or strengthened by it. The analytical results demonstrated that the second-order effect, associated with the progressive change in eccentricity of the tendons with increasing member deformation, is the main factor that distinguishes the behavior of external tendons from an internal unbonded tendon system. Because of this effect, undeviated external tendons mobilized lower nominal flexural resistance and inelastic deflections than did deviated tendons. When used for strengthening concrete flexural members, providing a moderate amount of external prestressing steel leads to significant deflection recovery, some reduction in the live load deflection, and a substantial increase in the yield load and ultimate flexural capacity of the members.

Exact Out-of-Plane Natural Frequencies of Curved Timoshenko Beams

Abstract: A powerful and efficient method is presented for finding exact out-of-plane natural frequencies of plane structures composed of curved Timoshenko beams. Initially, exact dynamic stiffnesses are derived from the governing differential equations of motion in a form that can be used directly in the stiffness method of analysis. This enables any appropriate structure to be modeled according to standard techniques, which, in this case, yield a transcendental eigenvalue problem. Then it is shown how any desired natural frequency may be obtained with certainty by employing a modification to a well-established algorithm, which ensures that no natural frequencies can be missed and avoids the usual approximations associated with traditional finite elements. Finally, comparisons are made with published results and an example shows how the natural frequencies of a continuous curved beam are altered when the effects of shear deflection and rotary inertia are considered.

INTRODUCTION TO OPERATING DEFLECTION SHAPES By

Abstract: Mode shapes and operating deflection shapes (ODS’s) are related to one another. In fact, ODS’s are always measured in order to obtain mode shapes. Yet, they are quite different from one another in a number of ways. In this paper, we will discuss ODS measurements, and their relationship to experimental modal parameters.

Concrete Beams with Openings: Analysis and Design

Abstract: Introduction General Classification of Openings Elastic Stress Distribution around Openings Design Considerations Beams with Small Openings General Pure Bending Bending and Shear Effect of Torsion Design for Torsion Effect of Coring Beams with Large Rectangular Openings General Analysis at Collapse Design for Ultimate Strength Crack Control Calculation of Deflection Multiple Openings Torsion in Beams with Large Rectangular Openings General Pure Torsion Torsion Combined with Bending Combined Torsion, Bending and Shear Analysis and Design of Continuous Beams General Elastic Analysis Design Procedure and Recommendations Design Example Effect of Prestressing General Stress Concentration and Stress Distribution Types of Cracking and Crack Control Deflections Design and Detailing for Ultimate Strength Appendices References Index

A mixed model for composite beams with piezoelectric actuators and sensors

Abstract: A theoretical formulation to model composite smart structures in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system is presented here. The mathematical model is based on a high order displacement field coupled with a layerwise linear electric potential. This model is developed for a composite beam structure using Hamilton's variational principle and is facilitated by the finite element (FE) formulation. The generic element implemented in the FE analysis is a two-noded Hermitian - 2(n+1) layerwise noded element for an n-layered beam. The variational principle led to a derivation that could include dynamic analysis but the present work will only focus on the static beam structure. This formulation in general will enable the modeling of vibration and shape control applications. Comparison of numerical results from this formulation with previous works, including three configurations - non-piezoelectric, actuator and sensor configurations, showed a high to a reasonable degree of correlation. The effects of varying actuator locations and orientations on the deflection and curvature of the beam were also studied.

Noise in piezoresistive atomic force microscopy

Abstract: The noise performance of piezoresistive atomic force microscopy (AFM) devices is investigated. The total deflection noise of a piezoresistive AFM device comprises vibrational noise from the cantilever, and Johnson and flicker noise from the piezoresistor. The vibrational deflection noise is found to have a minimum when the length of the piezoresistor is of the cantilever length. The minimum vibrational deflection noise is for a free cantilever, whereas a supported cantilever has a minimum vibrational noise of , where K is the spring constant of the device. Taking self-heating of the device into account, it is shown that an optimum power level exists at which the total equivalent displacement noise of a device is minimized. This minimum deflection noise is, for a fixed value of the spring constant, approximately proportional to the cantilever thickness, whereas it varies rather slowly with the length of the piezoresistor.

Thermal postbuckling of composite plates using the finite element modal coordinate method

Abstract: A finite element formulation in modal coordinates is developed for the nonlinear thermal postbuckling of thin composite plates. The linear buckling mode shapes used to model the postbuckling deflection are investigated. Postbuckling of symmetrically lami nated, antisymmetric angle-ply, and deflection of unsymmetrically laminated composite plates under mechanical and thermal loads are studied. Deflection shape changes are observed in a long rectangular plate. The participation from each mode to the postbuckling deflection is presented quantitatively. The results show that the modal-coordinate method can reduce the number of nonlinear equations dramatically and obtain accurate thermal postbuckling behavior.

Crack deflection in ceramic composites and fiber coating design criteria

Abstract: It is widely understood that the remarkable toughnesses demonstrated by some ceramic composites are dependent upon deflection of matrix cracks into fiber/matrix interfacial cracks. Carbon and BN fiber coatings are ideally suited for promotion of such crack deflection, but have the unfortunate weakness of limited oxidation resistance. The rational design of oxidation-resistant alternative fiber coatings is facilitated by consideration of the details of crack deflection, growth of interfacial cracks, and subsequent sliding along the interfacial crack surface. This work discusses some of these details and the implications regarding the design and testing of alternative fiber coating systems.

Localized damage response of composite sandwich plates

Abstract: The objective of this article is to derive closed-form solutions for the deformation and fracture responses of a composite sandwich plate subjected to static indentation of a hemispherical-nose indenter. The composite sandwich is modeled as an infinite, orthotropic, elastic plate resting on a rigid-plastic foundation. The facesheet deflection is several times the laminate thickness so that bending moments may be neglected and only membrane forces are considered in the facesheet. The rigid-plastic foundation force is given by the honeycomb crushing resistance. The deformation of the facesheet is found by using the principle of minimum potential energy. The elastic strain energy resulting from the membrane forces in the facesheet, the plastic work dissipated in crushing the honeycomb, and the external work are evaluated using an appropriate shape function for the facesheet deflection. The relations between the indentation load and the transverse deflection and length of deformation are obtained by minimization of the total potential energy. Minimization of the total potential energy has to be done numerically because of an implicit expression for the contact radius between the hemispherical-nose indenter and the facesheet of the honeycomb. An approximate solution for the load–indentation response is derived by assuming an average value of the contact radius. For the particular composite sandwich plates and indenters considered, the difference between the numerical and approximate solutions is about 3%. Furthermore, the approximate predictions are within 15% of the experimental results. Conservative estimates of the failure loads which cause cracking of the facesheet are predicted using the Maximum Stress and Tsai–Hill Criteria. The equations derived by the above failure criteria yield important design considerations for composite sandwich plates. It was observed that the failure load increases with the square of the ply thickness and indenter radius and is inversely proportional to the crushing resistance of honeycomb.

Fourier transform method for automatic processing of moire deflectograms

Abstract: In this work, a Fourier transform technique for automatic analysis of moire deflectograms is presented. A squared grating is used to multiplex the information of the deflection in two orthogonal directions in one image. This procedure avoids the necessity of rotating the gratings to obtain the complete deflection information. With this method only two fringe patterns. reference and distorted, are needed to determine the complete deflection information. To deal with irregularly shaped processing areas, a Gerchberg extrapolation method is used. The automatic determination of the carrier as well as the size and position of the reconstruction windows permit the complete and automatic measurement of the deflection produced by an ophthalmic lens in two orthogonal directions. Afterwards, the refractive power maps can be obtained, Experimental results obtained with a progressive addition lens are presented and comparison with measurements obtained with a commercial focimeter are shown showing a good agreement.

Analytical modeling and optimization for a laterally-driven polysilicon thermal actuator

Abstract: An electro-thermally and laterally driven microactuator is analytically examined which is based on the asymmetrical thermal expansion of the microstructure with different lengths of two beams. Deflection of the microactuator is modeled by the structural analysis. Analytical results are compared with the finite element model (FEM) results, and show a reasonable agreement. The magnitude of the deflection depends strongly on the geometry of the microactuator. The analytical model allows one to optimize efficiently the laterally driven thermal actuators.

Debonding of carbon-fibre-reinforced polymer plate from concrete beams.

Abstract: The overall aim of the study reported in this paper was to examine the plate-debonding phenomenon when carbon-fibre-reinforced polymer (CFRP) laminates are used as externally bonded additional reinforcement to strengthen reinforced concrete beam structural elements. The main variables investigated include the amount of tension reinforcement, the concrete strength, the amount of shear reinforcement and the location and arrangement of externally bonded anchorages. Six strengthened reinforced concrete beams, 150 × 250 × 3000 mm in size, with externally bonded unidirectiona CFRP laminates, were tested under four-point bending over an effective span of 2800 mm. The distinguishing feature in the design of the beams was the arrangement and location of the externally bonded anchorages. The beams were extensively instrumented, and deflection, concrete/ steel/plate strain and the plate-debonding process were continuously monitored during load testing to failure. The results of the tests were then critically analysed. It is shown that plate debonding in a sudden, brittle manner is a major problem associated with CFRP plate-bonding technology. Carefully designed external anchorages and lateral confinement of the compression zone are shown to be very effective in enhancing the overall performance of the strengthened beams and the utilization of the CFRP sheet.

Depth control of focused ion-beam milling from a numerical model of the sputter process

Abstract: A mathematical model of focused ion-beam milling is used to generate dwell times for the vector scanned pixel address scheme of a focused ion-beam deflection system. The model incorporates the absolute sputter yield of the solid as a function of the angle of incidence, and the relationship between the ion-beam current distribution and the pixel size of the deflection pattern. The object of this work is to be able to call for an arbitrary geometric shape to be ion milled and then have the numerical model compute the pixel dwell times for the deflection system such that the final cavity is sputtered. Experimental verification of the procedure was accomplished with parabolic troughs, hemispherical troughs, and cosine troughs. The term “trough” means a plane of symmetry in the ion-milled cavity. These same geometric shapes were also ion milled using a rotational axis of symmetry, yielding sinusoidal ring patterns, parabolic dishes, and hemispherical dishes. The absolute maximum depth for each of the cavities ...

The structural response of cylindrical shells to internal shock loading

Abstract: The internal shock loading of cylindrical shells can be represented as a step load advancing at constant speed. Several analytical models are available to calculate the structural response of shells to this type of loading. These models show that the speed of the shock wave is an important parameter. In fact, for a linear model of a shell of infinite length, the amplitude of the radial deflection becomes unbounded when the speed of the shock wave is equal to a critical velocity. It is evident that simple (static) design formulas are no longer accurate in this case. The present paper deals with a numerical and experimental study on the structural response of a thin aluminum cylindrical shell to shock loading. Transient finite element calculations were carried out for a range of shock speeds. The results were compared to experimental results obtained with the GALCIT 6-in. shock tube facility. Both the experimental and the numerical results show an increase in amplitude near the critical velocity, as predicted by simple steady-state models for shells of infinite length. However, the finite length of the shell results in some transient phenomena. These phenomena are related to the reflection of structural waves and the development of the deflection profile when the shock wave enters the shell.

Modeling of steel-concrete composite beams under negative bending

Abstract: Negative bending moments acting in the support regions of continuous composite beams generate tensile stresses in the concrete slab and compressive stresses in the lower steel profile. As a result the mechanical behavior of these beams is strongly nonlinear even for low stress levels, due not only to the slip at the beam-slab interface, but also to cracking in the slab. Therefore, an adequate theoretical modeling should take account of the interactions between the structural steel and the concrete slab by shear connectors and also between steel rebars and concrete in tension by bond phenomenon. In this paper a model of steel and concrete composite beams subjected to negative bending is presented. It accounts for the slip occurring at both the beam-slab interface and the steel reinforcement-concrete interface. Some numerical results, obtained using a suitable numerical procedure, are discussed to show the capacity of the model.