Non-symmetric Loading Research Articles

AN INTERFACE MODEL FOR ANALYSIS OF DEFORMATION BEHAVIOUR OF DISCONTINUITIES

An interface constitutive model is presented accounting for slip and sliding effects and also for dilatancy phenomena. The microslip effects are described by considering spherical asperity interaction with variation of contact area and generation of progressive or reverse slip zones. The incremental constitutive equations are derived with proper memory rules accounting for generation and annihilation of particular slip zones during the process of variable loading. It is further assumed that sliding of spherical contacts occurs along large asperities whose slope varies due to the wear process. The predicted shear and dilatancy curves are shown to provide close quantitative simulation of available experimental data The strain ratchetting effect for non-symmetric cyclic loading was exhibited using the asperity wear model. The model presented could be applied to simulate rock joints, masonry, or concrete cracked interfaces, under monotonic and cyclic loading.

Adaptive finite-element approach for analysis of bone/prosthesis interaction.

The study uses the finite-element method to analyse the stress field in a perfectly bonded hip prosthesis arising from loading through body weight. Special attention is paid to the accuracy of the numerical analysis, and adaptive mesh refinement is introduced to reduce the discretisation error. The finite-element procedure developed is especially well suited to analyse the behaviour of a bonded interface as it is capable of calculating accurately the stress at the nodal positions while satisfying the natural discontinuity in the stress field at this location. An orthotropic material model is used for the representation of the behaviour of the bone, and an axisymmetric geometry with non-symmetrical loading is adopted for the analysis. The results demonstrate the usefulness of adaptive mesh refinement and the significance of adopting anisotropic material modelling in the context of tissue/prosthesis interaction.

Temperature regime of slip bearings for cone bits under operating conditions

To design and fabricate cone bits, one must know how to predict the distribution of the temperature field in the supports of the roller bits. Theoretical calculation of nonstationary temperature fields under a nonsymmetric thermal loading is a separate serious mathematical problem. The edge conditions, and also certain system parameters of this problem are not precisely defined, since the temperature of the surrounding medium during drilling at great depths, the coefficient of friction in the bearings, and a number of other parameters, which cannot be assigned with the accuracy required for its solution, are unknown. Since it is currently impossible to obtain the temperature distribution in the bearing during drilling at great depths by experimental means, we decided to develop a computational-experimental method of determining the temperatures on the slip surfaces. The first stage of this method co~ists in the building of a mathematical model. The second stage consists in its experimental confirmation, which can be done during drilling at shallow depths. The third stage requires the development of a procedure for measuring the temperatures at individual points of the bits at great depths. The fourth stage involves determination of the temperature field using experimentally obtained temperature values at individual points and their use as edge conditions in the mathematical model. The problem statement for building a mathematical model of the temperature field in the body of a roller bit and journal assumes the following form. A system of bodies (shank journal and roller bit), which are in contact via friction surfaces (Fig. 1), is given; the heat sources are situated on the contact boundaries of the bodies (heat liberation in the bearings occurs as a result of friction). The thermophysical properties of the bodies and the initial temperatures on their perimeters are given. It is necessary to find the temperature distribution during operation of the bit on the contact surfaces of the bodies (the contact in the bearings). The problem can be resolved in the plane statement. The equation of nonstationary heat conduction in plane rigid bodies is

Toroidal shells under nonsymmetric loading

The complete asymptotic expansions of four homogeneous solutions, and a particular solution of toroidal shells, based on Novozhilov's thin shell equations, are given, which are valid for the stress and deformation of toroidal shells of circular cross section subjected to nonsymmetric loadings.

A Finite Element Model for Cables With Nonsymmetrical Geometry and Loads

A new two-dimensional finite element model is proposed for the deformation analysis of cable cross sections. The deformations of the cable cross section are of considerable design interest because of their effect on the induced torque or rotation of the cable. This model accounts for material orthotropy and nonsymmetrical geometry and loads. Each component of the cable is assumed to possess a circular cross section and is modeled as a macro-element having nodal degrees-of-freedom at all contact points with adjoining components. Usual finite element procedures are applied to solve for the unknown displacements at contact nodal points. The model is implemented in a computer code and is verified by test results obtained for an as-built cable.

Some unexpected properties of exact least-weight plane truss layouts with displacement constraints for several alternate loads

Basic geometrical properties of optimal plane truss layouts for multiple displacement constraints and several load conditions are derived. These include the feature that at any point, optimal bars may run in at most two directions and that even for two nonsymmetric alternative loads at the same point the optimal two-bar layout is always symmetrical for a vertical support. The above general findings are illustrated with examples, in which the results are derived by several independent methods, including a proof of global optimality of the layout.

Numerical analysis of a notched inelastic specimen and comparison with experimental results

The finite element method is used to determine the stress and strain distribution in a notched bar subjected to longitudinal nonsymmetric cyclic loading. The inelastic behaviour of the material is described by an incremental strain-rate independent constitutive model. The whole procedure is verified by comparing the calculated response with experimental results.

Asymmetric vibration of a heavily fluid‐loaded circular plate using variational principles

As an initial step in the extension of the surface variational principle (SVP) to an assumed modes analysis of vibratory displacement and surface pressure on submerged axisymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers an arbitrary harmonic excitation of an elastic plate. Two configurations, in which the supporting baffle is a thin rigid disk or an infinite plane, are considered. Fourier series expansions of the azimuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonic being governed by equations that are similar in form to those for the analogous axisymmetric problem. Recursion relations using coefficients developed in the course of solving the axisymmetric problem are shown to substantially expedite the evaluation of the additional azimuthal harmonics. Results for a force located at r=a/2 when ka=3.35, where a is the radius of the plate, are presented in terms of the radial variation associated with each harmonic, as wel...

Cavitation in elastic and elastic-plastic solids

I n this study, we examine the phenomenon of cavitation under non-symmetric loading. We seek all points in (τ 1, τ 2, τ 3)-stress space, such that, when the local principal true stress components (τ 1, τ 2, τ 3) at a particle reach a point on that set, cavitation ensues. This set can be described by a surface (τ 1, τ 2, τ 3) = 0 in stress space, which we refer to as a cavitation surface, and corresponds to a cavitation criterion that arises naturally from the analysis. By considering a particular subclass of the set of all kinematically admissible deformation fields, we determine an approximate analytical expression for by using the principle of virtual work. We explicitly determine and discuss the cavitation surface for a neo-Hookean material. We then consider the special case of axisymmetric cavitation corresponding to a stress state (τ 1, τ 2, τ 3), and illustrate our results for a neo-Hookean material and for a piccewisc power-law clastic-plastic material of the deformation theory. If cavitation occurs before yielding, we find that a good approximate criterion for cavitation is that it occurs when the mean stress τ m = (τ 1 + 2τ 2)/3 reaches a critical value, even if τ 1 ≠ τ 2; however, if cavitation is preceded by yielding, we find that this is not a good approximation. The accuracy of our approximate analytical results is assessed by comparing them with finite element results and the results of other researchers. The utility of the cavitation surface is illustrated by applying the cavitation criterion = 0 to two experimental settings.

Non-Symmetrical Loads in a Model Grain Bin During Eccentric Discharge

Eccentric discharge imposes non-symmetrical bin wall and floor loads. A series of tests were conducted for different eccentric discharge orifice locations. Floor loads during eccentric discharge of 0.61 m diameter model bin were smaller on the side nearest the discharge orifice than on the opposite side. The horizontal pressure distribution around the circumference of the bin wall depends on the height of grain above the floor.

3-D FE Stress Analyses of Mandible during biting.

In order to analyse stress distribution at the human mandible during biting, three dimensiona1finite element codes SAP6 and NISA II were employed. Two kinds of finite element models of mandibles symmetrical and nonsymmetrical shapes and load conditions determined by X-ray CT measurements were adopted to calculate the stress distribution. The computational results showed that the stress distributes in the entire area of these mandibles, but the stress around the condyle is less than the other regions. At the same time, Ca density distribution of the mandibles was measured by the same X-ray CT. These results showed strong relationship between stress and Ca density distributions.

Two-criterial evaluation of the limiting state of a cracked body under a nonsymmetric loading

Problems of the correct derivation of crack-resistance characteristics under longitudinal or transverse shear are examined. It is proposed that effective values of the stress intensity factor, which are calculated in accordance with the theory of maximum tensile stresses, can be used to calculate the limiting state and critical brittleness temperatures for a cracked body under a combined load. It is recommended that the limiting load of ductile failure be calculated in accordance with the theory of limiting equilibrium using the Tresca strength condition. An approximate method of plotting the weighting function for cracks subject to nonsymmetric loading is developed.

Verification of load distribution and strength of segmental post-tensioned concrete bridges

This paper outlines the use of several computer programs originally developed by Professor A. C. Scordelis for prediction of load distribution, deflections, and key internal stresses in segmentally constructed post-tensioned box girder bridges. Comparison with experimental results shows generally excellent agreement, even for highly non-symmetrical live load placement. In addition procedures for estimating the strength of such structures, including moment redistribution, are included.

Surface variational principle analysis of the response of an eccentrically loaded submerged disk in a baffle

As an initial step in the extension of the surface variational principle (SVP) to an assumed mode analysis of vibratory displacement and surface pressure on submerged axisymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers a harmonic point force applied at an arbitrary location of an elastic plate supported by an infinite, rigid baffle. Fourier series expansions of the azimuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonic being governed by equations that are similar in form to those for the analogous axisymmetric problem [J. H. Ginsberg, P. T. Chen, and A.D. Pierce, J. Acoust. Soc. Am. 88, 548–559 (1990)]. Recursion relations using coefficients developed in the course of solving the axisymmetric problem are shown to substantially expedite the evaluation of the additional azimuthal harmonics. Results for a force located at r=a/2 when ka = 3.35, where a is the radius of the plate, are presented in terms of the radial variation associated with each harmonic, as well as overall surface distributions. It is shown that m = 0 to m = 4 azimuthal harmonics are comparable in magnitude, and that other harmonics are insignificant. In addition, radiated power is evaluated as a function of m. [Work supported by ONR, Code 1132‐SA.]

Thermohydraulic Investigations of Decay Heat Removal Systems by Natural Convection for Liquid-Metal Fast Breeder Reactors

To examine the function of the safety-related SNR-2 decay heat removal concept, natural convection experiments were performed in two- and three-dimensional water models, scaled 1:20, under conditions of symmetric and nonsymmetric loads of the immersed coolers installed in the upper plenum at 180-deg positions with respect to each other. The temperature and velocity distributions were measured and the flow patterns recorded for different configurations of the instrumented plug.For symmetric load conditions, symmetric temperature and flow distributions were measured in two- and three-dimensional models. Nonsymmetric load conditions produce remarkable temperature differences between the two separated plenums of the two-dimensional model if fluid circulation is suppressed by a closed plug. An open plug allows fluid to pass through and shows lower temperature differences. In contrast, in the three-dimensional experiment, azimuthal fluid flow inside the plenum prevails even with the plug closed, and identical temperature distributions are measured. The calculations using the COMMIX-1B code are generally in good agreement with the measurements.

The elastic sphere under nonsymmetric loading

Existing solutions to boundary value problems arising from an elastic sphere subjected to a body force have been primarily restricted to axisymmetric, conservative loading. In this paper, a method for solving the displacement equations governing the static equilibrium of an elastic sphere subjected to an arbitrary body force and surface displacement is presented. The solutions are obtained in terms of three vector spherical harmonics and expressions for the displacement and stress fields are presented. Additionally, a short discussion indicating extension of these solutions to dynamic problems is included.

弾性基礎(Winkler基礎)上の円板の解析解

Both problems of bending considering transverse shear deformation and plane stress of circular plates on elastic foundation are discussed in this paper. The elastic foundation is assumed to be Winkler type. General solutions of the differential equations which govern these problems are presented as analytical solutions of the circular plates on elastic foundation under axi-symmetric and non-symmetric loading conditions. The well-known theory of Reissner is applied to the problems of bending considering transverse shear deformation. These presented solutions are formulated closed forms. They consist of the modified Bessel functions of the first kind of order n and so forth. It is very important to adopt displacement functions in order to obtain the analytical solutions for both problems of bending considering transverse shear deformation and plane stress of the circular plates on elastic foundation under non-symmetric loading conditions.

Performance analysis of finite capacity polling systems with nonexhaustive service

In performance investigations of token passing local area networks, communication subsystems in switching systems with distributed control, etc., the class of polling models, i.e., multiqueue systems with cyclic service, is often employed. This paper presents an approximate analysis method for this class of models, whereby realistic modelling assumptions like the finiteness of queue capacities and nonsymmetrical load conditions are taken into account. The method of imbedded Markov chain is used for the analysis, whereby the special case of exponential as well as the case of general service time are successively considered. The latter case is analyzed in conjunction with a moment matching approach for the cycle time. The validation of the approximation is done by means of computer simulations. Numerical results are shown in order to illustrate the accuracy of the calculation method and its dependency on system parameters.

Dynamics of frictionally constrained finite rod

A fractionally constrained finite rod subjected to nonsymmetric dynamic loading is analyzed. Due to dry friction a mass of the rod involved in the motion varies in time. For a rod modelled as a discrete mass system a computer simulation approach is developed. The simulation is used to identify the status of the physical system and the points in time when this status changes. The problem is reduced to a sequence of initial value problems and is solved by using the fitting method. A numerical example is given where it is shown that a slow motion of the rod can be induced in the case when the total external force (static plus dynamic) is smaller than the total friction force. For a particular five-mass model the domain of parameters for which the slow motion occurs is given.

An analysis of large deflections in a nonsymmetrical three-point bending of beams.

In a bending test of engineering materials such as spring steels and plastics, a fairly large deflection is observed without exceeding the elastic limit of materials. It is of great technological interest to know the large deflection behavior for various loading styles. This report deals with the problem of nonlinear large deflections of a thin elastic, three-point simply supported beam with a nonsymmetrical vertical load and gives analytical solutions for typical flexible quantities such as the deflection, arc length, curvature and bending stress. Moreover a large flexural bending test is carried out in order to confirm the applicability and reliability of the proposed theory. The experimental results are in good agreement with ones obtained by the analytical theory. Therefore the nonlinear large deflection theory presented here can be put into practical use.