Showing papers on "Deflection (engineering) published in 1993"

Theoretical analysis of the static deflection of plates for atomic force microscope applications

Abstract: The analysis of the static deflection of cantilever plates is of fundamental importance in application to the atomic force microscope (AFM). In this paper we present a detailed theoretical study of the deflection of such cantilevers. This shall incorporate the presentation of approximate analytical methods applicable in the analysis of arbitrary cantilevers, and a discussion of their limitations and accuracies. Furthermore, we present results of a detailed finite element analysis for a current AFM cantilever, which will be of value to the users of the AFM.

Analysis of tip deflection and force of a bimetallic cantilever microactuator

Abstract: The authors present a model of the electromechanical performance of bimetallic cantilever microactuators by deriving the relationship between the tip deflection and change in temperature using a simple analytical approach. The model is verified by comparison with finite element analysis and published experimental data. The maximum tip force generated by a bimetallic cantilever beam is calculated by finding the reaction force needed at the tip to prevent cantilever beam deflection.

Papermaking belt having semicontinuous pattern and paper made thereon

Abstract: A secondary belt for papermaking. The belt has a framework of protuberances arranged in a semicontinuous pattern to provide a semicontinuous pattern of deflection conduits. The semicontinuous pattern is distinguished from the discrete and continuous patterns of the prior art. The protuberances may be generally parallel, or may provide individual cells within the deflection conduits between the protuberances. Also disclosed is the paper made on such a secondary belt.

Dynamic Models for Structural Plasticity

Abstract: 1 Elastoplastic and Viscoplastic Constitutive Relations.- 2 Principles of Mechanics.- 3 Static Deflection.- 4 Dynamic Rigid-Plastic Response.- 5 Second-Order Effects on Dynamic Response.- 6 More Complex Configurations.- 7 Impact Experiments.

Buckling or transverse deflections of unsymmetrically laminated plates subjected to in-plane loads

Abstract: Numerous research publications purport to give in-plane buckling loads for unsymmetrically laminated composite plates. In many of these cases, bifurcation buckling is impossible; that is, transverse deflection is initiated, regardless of the magnitude of the loading. In the present work, finite element studies are made of four types of unsymmetrical laminates, including antisymmetrical ones. Twelve sets of edge constraints are considered. Maximum values of transverse deflection are determined for uniform and linearly varying in-plane boundary forces, including uniaxial, biaxial, and shear. Cases where the plate remains flat are thereby also identified. Results confirm a theoretical analysis previously made. Cases for which improper buckling results are often reported in the published literature are identified.

A Geometrically Nonlinear Theory of Elastic Plates

Abstract: A set of kinematical and intrinsic equilibrium equations are derived for plates undergoing large deflection and rotation but with small strain

Compliant Foil Bearing Structural Stiffness Analysis—Part II: Experimental Investigation

Abstract: This paper describes the second part of an investigation into the mechanism of deformation of the corrugated foil (bump foil) strips used in compliant surface foil bearings. In the earlier work, a theoretical model was developed to predict the structural characteristics of bump foil strips under various loads, including the effects of the friction forces between the compliant elements, local interaction forces, load distribution profiles, and bump configurations. In the experiments described here in, two-dimensional deflections of bump foils were recorded via an optical tracking system for a wide range of operating conditions to verify the feasibility of the theoretical model. Test results corroborate the theoretical model for the linear regions of load and the deflection parameters. The effects of the bearing design parameters, such as bump configuration, load profile, and surface coating and lubricant, on the structural characteristics of the bump foil strip were investigated. In addition, the source and mechanism of nonlinear behavior of the bump foil strips under light load conditions were examined, and more effective methods of achieving both Coulomb damping and optimum structural compliance were investigated. An understanding of the analytical and semi-empirical relations resulting from this work offers designers the potential for enhancing the design of high-performance compliant foil bearings.

Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle

Abstract: A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.

Flexural behavior of high-strength fiber reinforced concrete beams

Abstract: Eight high-strength concrete beams with different fiber contents and shear span-depth ratios were tested to study the influence of fiber addition on ultimate load, crack propagation, flexural rigidity, and ductility. The addition of steel fibers enhanced the strength and increased the ductility and flexural stiffness of the tested beams. A semi-empirical equation is proposed to estimate the effective moment of inertia of simply supported high-strength fiber reinforced concrete beams. The estimated deflections using this equation agree well with the experimental values. At ultimate conditions, the length of the plastic hinge developed was found to be proportional to the fiber content.

Elongation and load deflection characteristics of reinforced concrete members containing plastic hinges

Abstract: In regions, described as plastic hinge zones, in beams and columns, tensile yielding of the reinforcement through flexural action can occur in severe earthquakes. Where the beams and columns are lightly loaded, axially, member elongation can occur. Test results show that axial extensions of the order of several percent of the member depth may be expected. This deformation, which is ignored in current design practice, can have a major influence on the distribution of forces in a structure and its ability to survive without collapse. This paper describes the way in which elongation develops in plastic hinge zones together with the form of load deflection characteristics associated with the development of different types of plastic hinge zone.

Theoretical modeling of microfabricated beams with elastically restrained supports

Abstract: A mathematical model is developed to analyze the mechanical behavior of step-up supports which typically result from surface micromachining. This model accounts for the finite stiffness of the step-up support, which is more accurately represented by an elastically restrained boundary condition rather than a fixed or built-in boundary condition. Based on the model developed, the deflection of cantilever and doubly-supported beams under arbitrarily located concentrated and distributed loads is determined for a wide range of beam geometries. In addition, the buckling load of doubly-supported beams with elastically restrained boundary conditions is analyzed. Finite element analysis verifies the accuracy of the models developed. The models show that significant error in predicting the beam mechanical behavior may result if the finite stiffness of the step-up support is not correctly modeled. >

Elastica of cantilevered beams with variable cross sections

Abstract: Numerical and experimental methods are developed for solving the elastica of cantilevered beams of variable cross sections subjected to combined loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula — Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's horizontal deflection at the free end. Extensive numerical results, including deflected shapes and free-end rotations, are presented in non-dimensional form for elastic beams whose area moment of inertia (bending stiffness) varies linearly with beam length. In these studies, such beams are subjected to combinations of tip vertical loads, tip bending moments, and vertical distributed loads that vary linearly with beam length. Experimental studies are presented that complement the theoretical results.

Deflection of reinforced concrete members: a critical review

Abstract: Proposed code changes are presented for prediction of immediate and long-term change in length and deflections of reinforced concrete members with or without prestressing. The equations of ACI 318-89 and the Canadian standard CAN3-A23.3 are reviewed critically for prediction of immediate and long-term deflection in one-way nonprestressed construction. A more accurate approach is proposed that is not overly difficult to apply in practice.

Com624p--laterally loaded pile analysis program for the microcomputer, version 2.0. final report

Abstract: Computer Program COM624P has been developed for use in the analysis of stresses and deflection of piles or drilled shafts under lateral loads. The program is especially written for highway engineers who wish to run the analysis on microcomputers. The technology on which the program is based is the widely-used p-y curve method. The program solves the equations giving pile deflection, rotation, bending moment, and shear by using iterative procedures because of the nonlinear response of the soil. The program provides a user-friendly/menu-driven input and a graphics output in microcomputer environment. The version of the Program COM624P for the microcomputer was developed in 1989. Several new features were included in the program such as: generating p-y curves for rock, capability of analysis of piles in sloping ground, improved solution for multi-layered soils, and a variety of boundary conditions at the pile head for selection. The current version of COM624P (version 2.0) includes more improvements, and a subroutine has been added to compute the ultimate bending capacity and the flexural rigidity of piles. The user documentation provides detailed information to enable the user to employ the program conveniently and effectively. The documentation consists of three parts -- Part I, Users Guide; Part II, Engineering Background; and Part III, Systems Maintenance.

Micromachined silicon cantilever beam accelerometer incorporating an integrated optical waveguide

Abstract: A micromachined cantilever beam accelerometer is described in which beam deflection is determined optically. A diving board structure is anisotropically etched into a silicon wafer. This diving board structure is patterned from the wafer backside so as to leave a small gap between the tip of the diving board and the opposite fixed edge on the front side of the wafer. In order to sense a realistic range of accelerations, a foot mass incorporated onto the end of the beam is found to provide design flexibility. A silicon nitride optical waveguide is then deposited by low pressure chemical vapor deposition (LPCVD) onto the sample. Beam deflection is measured by the decrease of light coupled across the gap between the waveguide sections. In order to investigate sensor response and simulate deflection of the beam, we utilized a separate beam and waveguide section which could be displaced from one another in a precisely controlled manner. Measurements were performed on samples with gaps of 4.0, 6.0, and 8.0 micron and the variation of the fraction of light coupled across the gap as a function of displacement and gap spacing was found to agree with overlap integral calculations.

Finite Element Nonlinear Flutter and Fatigue Life of Two-Dimensional Panels with Temperature Effects

Abstract: A frequency domain method for two-dimensional nonlinear panel flutter with thermal effects obtained from a consistent finite element formulation is presented. von-Karman nonlinear strain-displacement relation is used to account for large deflections, and the quasisteady first-order piston theory is employed for aerodynamic loading. The panel motion under a combined thermal-aerodynamic loading can be mathematicall y separated into two parts and then solved in sequence: 1) thermal-aerodynamic static deflection (time-independent equilibrium position), and 2) limit-cycle oscillations. The finite element frequency domain results are compared with numerical time domain solutions. In a limit-cycle motion, the panel frequency and stress can be determined, thus fatigue life can be predicted. The influence of temperature and dynamic pressure on panel fatigue life is presented. Endurance and failure dynamic pressures can be established at a given temperature from the present method.

The prediction of the cutting force in ball-end milling with a flexible cutter

Abstract: In some situations, such as machining sculptured surfaces with long or slender ball-end mills, the cutter deflection in ball-end milling is a main factor affecting the machining accuracy. In this paper, a mechanistic cutting force prediction model of ball-end milling in consideration of cutter deflection is presented and its machining characteristics are discussed with experimental results. This model takes account of the changes in chip thickness by the deflection of a cutter and the cutter deflection is obtained by solving an equilibrium equation between cutting force and reaction force. The model was verified from the measurements of cutting forces for different machining conditions.

On the actual contribution of crack deflection in toughening platelet-reinforced brittle-matrix composites

Abstract: The effectiveness of crack deflection as a single toughening mechanism is evaluated in the case of brittle-matrix reinforced by high aspect-ratio platelets Microstructural parameters characterizing size, morphology, orientation and distribution of the second phase including aspect ratio, volume fraction and interparticle distance, were experimentally obtained by means of image analysis techniques on a model composite Introducing “true” microstructural parameters in the fracture mechanics formulation of the strain energy release rate for a deflected crack, it is demonstrated that no appreciable toughening can be obtained due to the geometrical local misalignment of the crack front even in the case of increasing aspect-ratio or volume fraction of second phase It is concluded that crack deflection processes may play an important role only as precursors for other operative mechanisms, being, in the general case, the deflection of the crack path only phenomenologically related to toughening

Dynamic Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility Model

Abstract: An approach for incorporating the heat transfer and elastic deformation effects into dynamic coefficient calculation is presented. A global analysis method is used, which finds the equilibrium pad till angles at each eccentricity position and includes cross-film variable viscosity, heat transfer effects in the lubricant, elastic deformation, heat conduction effects in the pads, and elastic deformation effect in the pivots. Deflection modes are used to approximate deformation of the top surface of the pads. The dynamic coefficients of a single pad are calculated at the equilibrium state of the bearing, based on numerical perturbation with respect to the bearing degrees of freedom. These include journal position, pad rotation, pivot deformation, and modal coordinates. The stiffness and damping coefficients are calculated and show very good agreement with experimental and numerical results from the existing literature

Modular ice protection assembly

Abstract: A modular ice protection system for an airfoil includes a deflection assembly attached to the airfoil and a removable outer shell having a modulus of elasticity of at least 40,000 kPa impermanently disposed over the deflection assembly, wherein the deflection assembly causes distortion of the separable outer shell during de-icing. The deflection assembly may likewise be removable from an underlying substructure which is attached to the airfoil.

Ignition resistant meltblown or spunbonded insulation material

Abstract: An ignition resistant fibrous material for use as insulation. The material comprises a multiplicity of meltblown or spunbonded thermoplastic filaments in combination with a multiplicity of nonlinear, nongraphitic carbonaceous fibers. The carbonaceous fibers have a Young's modulus of greater than 300,000 psi and reversible deflection ratio that is equal to or less than 1.2:1.