Showing papers on "Deflection (engineering) published in 2011"

Evaluation of Flexural Behavior and Serviceability Performance of Concrete Beams Reinforced with FRP Bars

Abstract: Flexural behavior and serviceability performance of 24 full-scale concrete beams reinforced with carbon-, glass-, and aramid-fiber-reinforced-polymer (FRP) bars are investigated. The beams were 3,300 mm long with a rectangular cross section of 200 mm in width and 300 mm in depth. Sixteen beams were reinforced with carbon-FRP bars, four beams were reinforced with glass-FRP bars, two beams were reinforced with aramid-FRP bars, and two were reinforced with steel, serving as control specimens. Two types of FRP bars with different surface textures were considered: sand-coated bars and ribbed-deformed bars. The beams were tested to failure in four-point bending over a clear span of 2,750 mm. The test results are reported in terms of deflection, crack-width, strains in concrete and reinforcement, flexural capacity, and mode of failure. The experimental results were compared to the available design codes.

Static pull-in analysis of microcantilevers based on the modified couple stress theory

Abstract: This paper investigates the deflection and static pull-in voltage of microcantilevers based on the modified couple stress theory, a non-classic continuum theory capable to predict the size effects for structures in micron and sub-micron scales. It is shown that the couple stress theory can remove the gap between the experimental observations and the classical theory based simulations for the static pull-in voltage.

Investigation of the size effects in Timoshenko beams based on the couple stress theory

Abstract: In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained for the axial deformation, bending deflection, and the rotation angle of cross sections in the static cases. As an example, the closed-form analytical results are obtained for the response of a cantilever beam subjected to a static loading with a concentrated force at its free end. The results indicate that modeling on the basis of the couple stress theory causes more stiffness than modeling by the classical beam theory. In addition, the results indicate that the differences between the results of the proposed model and those based on the classical Euler–Bernoulli and classical Timoshenko beam theories are significant when the beam thickness is comparable to its material length scale parameter.

Estimation of Tire-Road Friction Coefficient Using a Novel Wireless Piezoelectric Tire Sensor

Abstract: A tire-road friction coefficient estimation approach is proposed which makes use of the uncoupled lateral deflection profile of the tire carcass measured from inside the tire through the entire contact patch. The unique design of the developed wireless piezoelectric sensor enables the decoupling of the lateral carcass deformations from the radial and tangential deformations. The estimation of the tire-road friction coefficient depends on the estimation of slip angle, lateral tire force, aligning moment, and the use of a brush model. The tire slip angle is estimated as the slope of the lateral deflection curve at the leading edge of the contact patch. The portion of the deflection profile measured in the contact patch is assumed to be a superposition of three types of lateral carcass deformations, namely, shift, yaw, and bend. The force and moment acting on the tire are obtained by using the coefficients of a parabolic function which approximates the deflection profile inside the contact patch and whose terms represent each type of deformation. The estimated force, moment, and slip angle variables are then plugged into the brush model to estimate the tire-road friction coefficient. A specially constructed tire test rig is used to experimentally evaluate the performance of the developed estimation approach and the tire sensor. Experimental results show that the developed sensor can provide good estimation of both slip angle and tire-road friction coefficient.

Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory

Abstract: An electromechanical beam-type nano-actuator is one the most important smart nanostructures. In this paper, modified couple stress theory is used to model the size effect on the static pull-in instability of electrostatic nanocantilevers in the presence of dispersion (Casimir/van der Waals) forces. The monotonically iterative method (MIM) and homotopy perturbation method (HPM) are employed to solve the nonlinear constitutive equation of the nanostructure as well as numerical methods. Furthermore, a lumped parameter model is developed to explain the size-dependent pull-in performance of the nano-actuator. The basic engineering design parameters such as critical tip deflection and pull-in voltage of the nanostructure are computed. It is found that dispersion forces decrease the pull-in voltage and deflection of the nano-actuator at sub-micrometer scales. On the other hand, the size effect can increase the pull-in parameters of the nano-actuators. The results indicate that the proposed analytical solutions are reliable for simulating nanostructures at sub-micrometer ranges.

Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms

Abstract: This paper explores the deflection and buckling of fixed-guided beams used in compliant mechanisms. The paper's main contributions include the addition of an axial deflection model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models typically incorrectly predict a beam's buckling mode unless unrealistic constraints are placed on the beam. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force versus displacement predictions of the model are compared to the experimental force versus deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force versus deflection data for each device.

Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces

Abstract: This paper investigates the pull-in instability of micro-switches under the combined electrostatic and intermolecular forces and axial residual stress, accounting for the force nonlinearity and geometric nonlinearity which stems from mid-plane stretching. The micro-switch considered in the present study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Theoretical formulations are based on Euler–Bernoulli beam theory and von Karman type nonlinear kinematics. The principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using the differential quadrature method (DQM). Pull-in voltage and pull-in deflection are obtained for micro-switches with four different boundary conditions (i.e. clamped–clamped, clamped-simply supported, simply supported and clamped-free). The present solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted, focusing on the combined effects of geometric nonlinearity, gap ratio, slenderness ratio, Casimir force, axial residual stress and material composition on the pull-in instability.

A discrete particle approach to simulate the combined effect of blast and sand impact loading of steel plates

Abstract: The structural response of a stainless steel plate subjected to the combined blast and sand impact loading from a buried charge has been investigated using a fully coupled approach in which a discrete particle method is used to determine the load due to the high explosive detonation products, the air shock and the sand, and a finite element method predicts the plate deflection. The discrete particle method is based on rigid, spherical particles that transfer forces between each other during collisions. This method, which is based on a Lagrangian formulation, has several advantages over coupled Lagrangian–Eulerian approaches as both advection errors and severe contact problems are avoided. The method has been validated against experimental tests where spherical 150 g C-4 charges were detonated at various stand-off distances from square, edge-clamped 3.4 mm thick AL-6XN stainless steel plates. The experiments were carried out for a bare charge, a charge enclosed in dry sand and a charge enclosed in fully saturated wet sand. The particle-based method is able to describe the physical interactions between the explosive reaction products and soil particles leading to a realistic prediction of the sand ejecta speed and momentum. Good quantitative agreement between the experimental and predicted deformation response of the plates is also obtained.

Analysis of Cracks and Deformations in a Full Scale Reinforced Concrete Beam Using a Digital Image Correlation Technique

Abstract: This paper deals with the use of a digital image correlation technique for the determination of the actual mechanical behaviour of a full scale reinforced concrete beam after 25 years of service in a severe industrial environment. The objective is to investigate the influence of the service conditions on the cracking process and the flexural behaviour of the beam. For this purpose, one beam is removed from the existing structure before being tested in four point bending in laboratory. Displacement fields derived from digital images captured during five loading cycles are analysed in terms of crack detection and measurement, beam deflection and curvature. Owing to its good resolution, the method proves suitable for early crack detection and measurement. A comparison between experimental results and theoretical values derived from Eurocode 2 design code in the serviceability state suggests the existence of a longitudinal compressive force in the beam. A complementary analysis confirms the validity of this hypothesis. It is concluded that the cracking and the flexural behaviour of the tested beam are significantly affected by the existence of an initial compressive stress, which is possibly resulting from a swelling of the concrete due to long term exposure to wet atmosphere and elevated temperature.

Tool deflection and geometrical error compensation by tool path modification

Abstract: Accuracy of CNC machined components is affected by a combination of error sources such as tool deflection, geometrical deviations of moving axis and thermal distortions of machine tool structures. Some of these errors can be decreased by controlling the machining process and environmental parameters. However other errors like tool deflection and geometrical errors that have a big portion of total error need more sophisticated solutions. Conventional error reduction methods are considered as low efficiency and human dependent methods. Most of recently developed solutions cannot fulfill workshop needs and are limited to research papers. In the present study, machining code modification strategy has been considered as an applicable and effective solution to enhance precise machined components. Appropriate tool deflection estimation model as well as geometrical error analyzing methods have been selected and complementary algorithms for compensation of these errors have been developed. Metal cutting process has been modeled in a 3D simulation environment and implemented in force/deflection calculations. A software has been developed to generate compensated tool path NC program by tracing the initial tool path and compensating deflection/geometry deviations. The new procedure developed in the present work has been validated by machining Spline contours. The results show that using the new method, accuracy of machined features can be improved by about 8–10 times in a single pass.

Equivalent Moment of Inertia Based on Integration of Curvature

Abstract: This paper evaluates the benefits of computing deflection with an equivalent moment of inertia based on integration of curvature to account for changes in member stiffness along the span. Results are evaluated for steel and fiber-reinforced polymer reinforced (FRP-reinforced) concrete flexural members with different loading arrangements and support conditions. Closed-form solutions of integrated expressions for deflection are expressed in terms of an equivalent moment of inertia Ie′ and compared to deflection computed with an effective moment of inertia Ie based on the stiffness at the critical section. Results from this comparison are validated with measured deflections from an experimental database for FRP-reinforced concrete. Current code-related approaches are also compared to the experimental database. It is shown herein that the use of an integration-based expression for the moment of inertia can lead to improved prediction of deflection, though the use of an effective moment of inertia based on mem...

Aircraft control surface deflection using RBF-based mesh deformation

Abstract: In this paper, mesh deformation based on radial basis function (RBF) interpolation is applied to the deflection of aircraft control surfaces. A confinement technique is presented, which locally restricts mesh deformation to the vicinity of the moving component and leaves the surfaces of other components unaffected. This technique is shown to have the potential to significantly reduce the CPU time necessary for evaluating the RBF interpolants. Motivated by the directionality of control surface deflection, the idea of treating each direction of the displacements separately is introduced. It is employed for the adaptive selection of centers, and the approach termed sequential uni-variate center adaptation. It is shown to be more efficient for both solution and evaluation processes than the standard approach, in which the same set of centers is used for every direction. Furthermore, different data sites may be imposed for different directions. It is demonstrated that this enables sliding motion of the elements on the face of a mesh block. Thereby, large control surface deflections are possible, despite the presence of a small spanwise gap between control surface and parent component. These techniques are successfully applied to the deflection of aileron and horizontal tail of a generic fighter aircraft configuration.

Size effect in micro-scale cantilever beam bending

Abstract: When the thickness of metallic cantilever beams reduces to the order of micron, a strong size effect of mechanical behavior has been found. In order to explain the size effect in a micro-cantilever beam, the couple-stress theory (Fleck and Hutchinson, J Mech Phys Solids 41:1825–1857, 1993) and the C-W strain gradient theory (Chen and Wang, Acta Mater 48:3997–4005, 2000) are used with the help of the Bernoulli–Euler beam model. The cantilever beam is considered as the linear elastic and rigid-plastic one, respectively. Analytical results of the cantilever beam deflection under strain gradient effects by applying these two kinds of theories are obtained, from which we find an explicit relationship between the intrinsic lengths introduced in the two kinds of theories. The theoretical results are further used to analyze the experimental observations, and predictions by both theories are further compared. The results in the present paper should be useful for the design of micro-cantilever beams in MEMS and NEMS.

Energy scavenging from insect flight

Abstract: This paper reports the design, fabrication and testing of an energy scavenger that generates power from the wing motion of a Green June Beetle (Cotinis nitida) during its tethered flight. The generator utilizes non-resonant piezoelectric bimorphs operated in the d31 bending mode to convert mechanical vibrations of a beetle into electrical output. The available deflection, force, and power output from oscillatory movements at different locations on a beetle are measured with a meso-scale piezoelectric beam. This way, the optimum location to scavenge energy is determined, and up to ∼115 μW total power is generated from body movements. Two initial generator prototypes were fabricated, mounted on a beetle, and harvested 11.5 and 7.5 μW in device volumes of 11.0 and 5.6 mm 3 , respectively, from 85 to 100 Hz wing strokes during the beetle’s tethered flight. A spiral generator was designed to maximize the power output by employing a compliant structure in a limited area. The necessary technology needed to fabricate this prototype was developed, including a process to machine high-aspect ratio devices from bulk piezoelectric substrates with minimum damage to the material using a femto-second laser. The fabricated lightweight spiral generators produced 18.5‐22.5 μ Wo n a bench-top test setup mimicking beetles’ wing strokes. Placing two generators (one on each wing) can result in more than 45 μW of power per insect. A direct connection between the generator and the flight muscles of the insect is expected to increase the final power output by one order of magnitude. (Some figures in this article are in colour only in the electronic version)

Evaluation of length-scale effects for mechanical behaviour of micro- and nanocantilevers: II. Experimental verification of deflection models using atomic force microscopy

Abstract: This paper is the second of two parts that reports on evaluating the length-scale effects for micro- and nano-sized silicon cantilevers using experimental data provided by atomic force microscopy. The tip deflections estimated with the conventional tip deflection model and the modified deflection model incorporating the length-scale factor are determined and compared with the experimental data. These comparative data demonstrate that the length-scale factor should be considered in accurately estimating the tip deflection of the micro- and nano-sized cantilevers. We also present the effect of the length-scale factor on the stiffness of the cantilevers, which also indicate that the classical models derived for macro-sized cantilevers cannot be used to accurately estimate the bending stiffness of the micro- and nano-sized cantilevers. The implications of accurately estimating the tip deflection and stiffness for micro- and nanocantilever sensors are discussed and it is concluded that when these sensors are used in the static mode, the modified deflection model should be used in estimating the mass of the species of interest binding (analyte) on the surface of the cantilevers.

Steerable endoluminal devices and methods

Abstract: A steerable endoluminal device adapted for delivery into a patient's vasculature. The device includes a tubular member having a distal deflection portion that extends to the distal end and a main body portion that extends from the deflectable portion to the proximal end, the tubular member further including a stiff portion extending along the distal deflection portion, and being formed of polymeric material, which is disposed circumferentially adjacent to the stiff portion. The stiff portion is made of a material that has an elastic modulus greater than the elastic modulus of the polymeric material. A pull wire extends between the proximal end and the distal end of the tubular member and is attached to the distal deflection portion to control deflection of the distal deflection portion of the tubular member.

Investigating new symmetry classes in magnetorheological elastomers: cantilever bending behavior

Abstract: This work defines and examines four classes of magnetorheological elastomers (MREs) based upon permutations of particle alignment‐magnetization pairs. Particle alignments may either be unaligned (e.g. random) or aligned. Particle magnetizations may either be soft-magnetic or hard-magnetic. Together, these designations yield four material types: A‐S, U‐S, A‐H, and U‐H. Traditional MREs comprise only the A‐S and U‐S classes. Samples made from 325-mesh iron and 40 μm barium hexaferrite powders cured with or without the presence of a magnetic field served as proxies for the four classes. Cantilever bending actuating tests measuring the magnetically-induced restoring force at the cantilever tip on 50 mm × 20 mm × 5 mm samples yielded ∼350 mN at μ0 H = 0.09 T for classes A‐H, A‐S, and U‐S while class U‐H showed only ∼40 mN. Furthermore, while classes U‐S and A‐S exerted forces proportional to tip deflection, they exerted no force in the undeformed state whereas class A‐H exerted a relatively constant tip force over its entire range of deformation. Beam theory calculations and models with elastic strain energy density coupled with demagnetizing effects in the magnetic energy density were used to ascertain the magnitude of the internal bending moment in the cantilever and to predict material response with good results. This work highlights the ability of the newly developed A‐H MRE materials, and only that material class, to operate as remotely powered bidirectional actuators. (Some figures in this article are in colour only in the electronic version)