Showing papers on "Bending moment published in 2002"

Refined plate theory and its variants

Abstract: Thedevelopmentofa newree ned platetheoryand its two simplevariantsisgiven. Thetheorieshavestrongcommonality withtheequationsofclassicalplatetheory (CPT).However,unlikeCPT,thesetheoriesassumethatlateral and axial displacements have bending and shear components such that bending components do not contribute toward shearforces and, likewise, shearing components do not contribute toward bending moments. The theory and one of its variants are variationally consistent, whereasthesecond variant isvariationally inconsistent and usesthe relationships between moments, shear forces, and loading. It should be noted that, unlike any other ree ned plate theory, thegoverning equation as well as the expressions for moments and shear forces associated with thisvariant areidentical tothoseassociated withtheCPT,savefortheappearanceofasubscript. Theeffectivenessofthetheory and itsvariantsisdemonstratedthroughanexample. Surprisingly,theanswersobtained by boththevariantsofthe theory, one of which is variationally consistent and the other one is inconsistent, are same. The numerical example studied, therefore, not only brings out the effectiveness of the theories presented, but also, albeit unintentionally, supports the doubts, e rst raised by Levinson, about the so called superiority of variationally consistent methods.

Large deflections of cantilever beams of non-linear elastic material under a combined loading

Abstract: Large deflection of cantilever beams made of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. Governing equation was derived by using the shearing force formulation instead of the bending moment formulation because in the case of large deflected member, the shearing force formulation possesses some computational advantages over the bending moment formulation. Since the problem involves both geometrical and material non-linearities, the governing equation is complicated non-linear differential equation, which would in general require numerical solutions to determine the large deflection for a given loading. Numerical solution was obtained by using Butcher's fifth order Runge–Kutta method and are presented in a tabulated form.

Uncertainties in Material and Geometric Strength and Load Variables

Abstract: Uncertainty in the basic load and strength variables of a ship structure can significantly affect structural performance and safety. Variations in strength, load and load effects greatly impact the reliability of a structural system. Understanding and including this variation, or uncertainty, in the design and analysis of ship structures requires the use of structural reliability-based design and assessment methodologies. For example, the design strength is based on nominal values for variables such as yield stress of the material, plate thickness, modulus of elasticity, etc. The actual values of these variables are often different from the nominal, or design, values. These actual values tend to behave in a random manner, causing random behavior of the actual structural strength. Understanding the randomness of the basic strength variables allows the designer to account for this variability in the design strength of the structure. The moment methods for calculating reliability-based, partial safety factors (Ang and Tang 1984 and Ayyub and White 1987) require probabilistic characteristics of both strength and load variables in the limit state equation. Relevant strength variables for ship plates are the material's yield strength (stress)(Fy), modulus of elasticity (E), Poisson's ratio (v), thickness (t), and length (a) and width (b) of a plate. The relevant load variables are the external pressures due to stillwater bending moment, wave bending moment, and dynamic loads. Uncertainty, reliability, and risk measures are vital to the analysis and design of an engineering system. The reliability of the system can be stated in reference to some performance criteria. The need for reliability analysis stems from the fact that there is the presence of uncertainty in the definition, understanding, modeling, and behavior prediction of the model or models describing the system. The objective herein is to compile statistical information and data based on literature review on both strength and load random variables relevant to ship structures for quantifying the probabilistic characteristics of these variables.

Hydroelastic behaviour of compound floating plate in waves

Abstract: The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.

Commercial aircraft low cost, lightweight floor design

Abstract: An aircraft deck support system includes horizontal deck support beams connected to the aircraft's frames. Each deck support beam has a plurality of machined, generally T-shaped supports. Each T-shaped support includes either a horizontal recess or a raised surface formed in a deck support beam upper chord and a U-shaped aperture formed in a beam web. The T-shaped support matably receives a cross-support beam attachment flange perpendicularly aligned with the deck support beams. Each cross-support beam includes a web perpendicularly connected at an upper end to the attachment flange, and a stiffening flange at a web lower end. Both the web and the stiffening flange are freely suspended within the U-shaped aperture of the T-shaped support. When joined, the cross-support beam seats on the T-shaped support allowing both the cross-support beam and the deck support beam to develop maximum bending moments at a reduced structural weight.

An investigation of the fatigue and fretting performance of a representative aero-engine spline coupling

Abstract: The fatigue behaviour of a representative high-performance aero-engine spline coupling is investigated under test conditions designed to simulate in-service conditions. The test load cycles consist of major cycle torque and axial load, simulating maximum thrust, combined with minor cycle rotating bending moment and fluctuating torque, simulating life-limiting conditions at take-off. The objective of the study is to develop understanding of the fatigue behaviour of the coupling over a range of loading conditions, including interaction between low-cycle fatigue, fretting fatigue and fretting wear. This information is necessary for the development of fatigue and fretting-fatigue life prediction techniques. The test results are interpreted with the help of three-dimensional finite element models, which include the frictional contact between the spline teeth.

Comparison of numerical and experimental results of nonlinear wave-induced vertical ship motions and loads

Abstract: A nonlinear time-domain procedure is presented which is used to calculate the vertical responses of a container ship advancing in head waves. The method assumes linear radiation forces represented by time convolution of memory functions, infinite frequency added masses, and radiation restoring coefficients. The nonlinear hydrostatic restoring and Froude–Krilov forces are computed exactly over the instantaneous wetted surface of the ship's hull. Forces due to green water on deck are calculated using the momentum method. Nonlinear effects are identified on different vertical ship responses, namely on the heave and pitch motions, the vertical accelerations, and the vertical bending moment. These non-linear effects are expressed by the variation of the transfer function with the wave amplitude, the higher-order harmonics of the time signals, the offset of the time series, and the asymmetry of the peaks. The numerical results and the quantified nonlinear effects are compared with experimental results showing an ability to reproduce the main nonlinear effects.

A Biomechanical Model of the Foot: The Role of Muscles, Tendons, and Ligaments

Abstract: A biomechanical model of the foot is developed and analyzed to determine the distribution of support under the metatarsal heads, the tension in the plantar aponeurosis, and the bending moment at each of the joints of the foot. This model is an extension of our earlier work to include the role of muscles, tendons, and ligaments. Two cases are presented: in the first the center of gravity of the body is over the mid foot, and in the second, the center of gravity is anterior, over the metatarsals, and no support is provided by the heel. The model shows the extent to which the muscles reduce the force in the supporting ligaments at each of the joints and decrease the tension in the plantar aponeurosis, and that this effect is more pronounced when the center of gravity of the body is moved forward.

Sensor device, in particular for a prosthesis, and prosthesis having such a sensor device

Abstract: A sensor device (15) for a prosthesis, in particular for a leg prosthesis, is provided for measuring forces acting on the prosthesis, having a ring-shaped outer member (16) of closed construction and an inner member (21, 22) connecting two opposite inner sides (17 a, 17 b) of the outer member having a sensor element (31) for measuring the force acting in the direction of the connecting axis. The outer member deforms under the action of a bending moment while the inner member (21) feels only the axial force acting in the direction of its connecting axis. By this means measurement of the axial force unaffected by bending moments is possible. Furthermore, the sensor device is able to transmit loads.

Mode Shape Corrections for Wind Load Effects

Abstract: Traditionally, wind analysis procedures based on the ''gust loading factor'' approach and experimental techniques involving the high frequency base balance and the ''stick-type'' aeroelastic model test have assumed ideal structural mode shapes, i.e., linear lateral modes and uniform torsional modes. The influence of nonideal mode shapes manifests itself through modifications in the generalized wind load, the structural displacement, the equivalent static wind load ~ESWL!, and the attendant influence function. This has led to the introduction of several correction procedures, each focusing on an individual feature of the overall response analysis framework. This paper presents a systematic development of correction procedures in terms of correction factors ~CFs! to account for nonideal mode shapes in the formulation of generalized load, analysis of structural response, and the derivation of the ESWL. A parameter study is conducted to examine the significance of CFs in estimating various load effects. It is observed that the influence of a nonideal mode shape is actually negligible for the displacement response and the base bending moment, but not so for other load effects, e.g., the base shear and the generalized wind load. Although the existing procedures are effective in correcting the intended response component, they should not be used indiscriminately for other load effects. This paper also presents a correction procedure for the influence of mode shapes on the ESWLs, a loading format that is very attractive for implementation in codes and standards and design practice as well as for the correct interpretation of wind tunnel measurements.

Finite Bending of a Rectangular Block of an Elastic Hencky Material

Abstract: Hencky's elasticity model is an isotropic, finite hyperelastic equation obtained by simply replacing the Cauchy stress tensor and the infinitesimal strain tensor in the classical Hooke's law for isotropic infinitesimal elasticity with the Kirchhoff stress tensor and Hencky's logarithmic strain tensor. A study by Anand in 1979 and 1986 indicates that it is a realistic finite elasticity model that is in good accord with experimental data for a variety of engineering materials for moderate deformations. Most recently, by virtue of well-founded physical grounds and rigorous mathematical procedures it has been demonstrated by these authors that this model may be essential to achieving self-consistent Eulerian rate type theories of finite inelasticity, e.g., the J 2-flow theory for metal plasticity, etc. Its predictions have been studied for some typical deformation modes, including extension, simple shear and torsion, etc. Here we are concerned with finite bending of a rectangular block. We show that a closed-form solution may be obtained. We present explicit expressions for the bending angle and the bending moment in terms of the maximum or minimum circumferential stretch in a general case of compressible deformations for any assigned stretch normal to the bending plane. In particular, simplified results are derived for the plane strain case and for the case of incompressibility.

Prefabricated shearwall having improved structural characteristics

Abstract: A novel prefabricated shearwall is disclosed with improved structural characteristics in terms of its ability to 1) transfer lateral loads to the foundation, 2) resist bending moments normally arising in conventional shearwalls between hold-down hardware and end posts or vertical framing members, 3) effectively diffuse stresses known to result in nail fatigue, and 4) reduce slippage between the bottom of the end posts and base in response to cyclic loadings. These superior properties result partly from its geometry in lower, or shear force transfer region, accompanied by thrust block/anchor rod assemblies to provide stiffness and strength over the lower portion of the end posts. Furthermore, specialized wrap-around connector plates that cover a portion of the bottom surface of these end posts also contribute to the enhanced prefabricated shearwall design.

Decay Rates for a Beam with Pointwise Force and Moment Feedback

Abstract: We consider the Rayleigh beam equation and the Euler–Bernoulli beam equation with pointwise feedback shear force and bending moment at the position ξ in a bounded domain (0,π) with certain boundary conditions. The energy decay rate in both cases is investigated. In the case of the Rayleigh beam, we show that the decay rate is exponential if and only if ξ/π is a rational number with coprime factorization ξ/π=p/q, where q is odd. Moreover, for any other location of the actuator we give explicit polynomial decay estimates valid for regular initial data. In the case of the Euler–Bernoulli beam, even for a nonhomogeneous material, exponential decay of the energy is proved, independently of the position of the actuator.

Three-dimensional finite element analysis of single-lap adhesive joints subjected to impact bending moments

Abstract: This paper deals with the stress wave propagations and stress distributions in single-lap adhesive joints subjected to impact bending moments with small strain rate. The elastic stress wave propagation and the stress distribution in single-lap adhesive joints of similar adherends subjected to impact bending moments are analyzed using three-dimensional finite-element method (FEM). A three-point impact bending moment is applied to the joint by dropping a weight. FEM code employed is DYNA3D. The effects of Young's modulus of the adherends, the lap length, the adherend thickness and the adhesive thickness on the stress wave propagation at the interfaces are examined. It is found that the maximum value of the maximum principal stress, σ1, appears at the interface between the adhesive and the upper surface of upper adherend which is impacted. The maximum stress, σ1, increases as Young's modulus of adherends, the lap length and the adhered thickness increase. It is also found that the maximum stress, σ1 increase...