Arbitrary Load Distribution Research Articles

Admissible shell internal forces and safety assessment of masonry domes

The present paper illustrates a methodology for the safety assessment of masonry domes. The dome is modelled as a thin shell made of a material satisfying Heyman’s hypotheses. Based on the static theorem of limit analysis, the method searches for statically admissible distributions of internal forces within the shell, suitably combining membrane forces and bending moments, by solving a convex optimisation problem. The solution is pursued numerically by means of an expressly developed collocation method that enables obtaining the analytical expressions for each internal force component. In its present formulation the method can be applied to domes of any shape, as well as to arbitrary load distributions. After validation against the benchmark case of the spherical dome under its self-weight, the paper illustrates application of the method to the dome of Pisa Cathedral under vertical loads as a first real case study.

Discrete load balancing on complete bipartite graphs

We study the process of balancing m indivisible tokens among n nodes connected by a complete bipartite graph. The load of a node at time t is the number of tokens the node stores at that time. Initialized with an arbitrary load distribution of the tokens, in each time step, an edge of the graph is randomly selected, and the two endpoint nodes exchange tokens such that their loads are balanced as evenly as possible. A balance is the state where all nodes have nearly the same number of tokens. We prove that, with high probability, this process reaches an almost perfect balance after O(nlog⁡Δ+n1n2log⁡n) steps, where n1 and n2 are the vertex number of the two independent sets in the bipartite graph, and Δ is the maximum initial load difference between two nodes.

Distributed programming of a hyperspectral image registration algorithm for heterogeneous GPU clusters

Hyperspectral image registration is a relevant task for real-time applications such as environmental disaster management or search and rescue scenarios. The HYFMGPU algorithm was proposed as a single-GPU high-performance solution, but the need for a distributed version has arisen due to the continuous evolution of sensors that generate images with finer spatial and spectral resolutions. In a previous work, we simplified the programming of the multi-device parts of an initial MPI+CUDA multi-GPU implementation of HYFMGPU by means of Hitmap, a library to ease the programming of parallel applications based on distributed arrays. The performance of that Hitmap version was assessed in a homogeneous GPU cluster. In this paper, we extend this implementation by means of new functionalities added to the latest version of Hitmap in order to support arbitrary load distributions for multi-node heterogeneous GPU clusters. Three different load balancing layouts are tested, which prove that selecting a proper layout affects the performance of the code and how this performance is correlated with the use of the GPUs available in the cluster.

Closed-Form Calculation of Lead Flank Modification Proposal for Spur and Helical Gear Stages

Abstract Due to the growing need for gearboxes to be as lightweight and efficient as possible, it is most important that the gear mesh’s potential is utilized as well as possible. One way of doing that is to define a flank modification that optimally distributes the load over the flank. Best practice for defining a flank modification is to manually check out the load distribution and to define a value of the flank modification. In general, this is an iterative method to get an optimally distributed load. This method can also be automated. To do this, the deformations of the gearbox (shafts, bearings, gear mesh) are calculated. With those results, a modification proposal is calculated and applied to the calculation model. As soon as the values for the next additional modification proposal drop under a certain limit, the iteration is finished. This method consumes time and computing power. Additionally, since it is an iteration, it does not always converge. A new method for calculating the lead flank modification for all gear stages in the gearbox to be calculated is presented in this paper. The method shown in this paper uses additional degrees of freedom and equations, which are integrated into the linear equation system of the gearbox model. Those degrees of freedom and the equations apply the boundary condition to the model of a constant load distribution. By introducing additional factors in the equations, it is possible to calculate a lead flank modification for an arbitrary load distribution. By integrating these additional degrees of freedom and the equations, only one additional calculation is needed to get a modification proposal. Examples throughout this paper show the results of this method.

АВТОМАТИЧЕСКАЯ СИНХРОНИЗАЦИЯ «ОСТРОВОВ» ПРИ ВОССТАНОВЛЕНИИ СИСТЕМ ЭЛЕКТРОСНАБЖЕНИЯ С РАСПРЕДЕЛЕННОЙ ГЕНЕРАЦИЕЙ

The PURPOSE of the paper is to develop an operation algorithm of the automatic synchronization system under the restoration of the power supply system after emergency cut-off from the main power source (MPS) and breaking of the power supply system into separate “islands”. METHODS. Some operation stages of the synchronization system use reachability matrices, for the construction of which the Floyd-Warshall algorithm is used. RESULTS AND THEIR DISCUSSION. The operation of the synchronization system using the proposed algorithm is demonstrated on the test scheme of the power supply system. The execution of the algorithm is triggered in case of emergency shutdown of current breakers (CB); the algorithm identifies the structure of the “islands” formed as a result of the accident and forms a definite order of the synchronization process; the error signals determined by the algorithm are applied to automatic speed regulators (ASR) and automatic voltage regulators (AVR) of distributed generators (DG); when the synchronism is achieved the algorithm generates the commands to switch on the current breakers. CONCLUSIONS. The proposed algorithm of the synchronization system allows to reconnect the “islands” formed as a result of the accident between each other and with the main power source. When the power supply system is disconnected from the main power source it is necessary to switch the automatic speed regulators of distributed generators to a floating response to eliminate the frequency deviation from the nominal one. In order to exclude an arbitrary load distribution between the distributed generators when the automatic speed regulators are switched to a floating response it is necessary to use a group control of active and reactive power.

An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model

A three-dimensional lumped-parameter model for a pair of helical gears is developed and shown to be equivalent to an arbitrary tooth contact force distribution. The nonlinearity of the gear mesh is due to portions of gear teeth contact lines losing contact (partial contact loss). The lumped-parameter model accounts for the net force and moment arising from an arbitrary load distribution including partial contact loss. This model is shown to be equivalent to a four-parameter model defined by a translational stiffness acting at the center of stiffness and a twist stiffness. The twist stiffness generates a moment, which is solely due to the spread of contact across the tooth face. The movement of the translational stiffness across the tooth face generates an additional moment. The four parameters in the model are useful post-processing output quantities to track and interpret the gear mechanics and the mesh forces and moments that develop under static or dynamic conditions.The translational and twist stiffnesses and the center of stiffness depend strongly on the relative translation and twist at the gear mesh, introducing nonlinearity. Tooth surface modifications smoothen the translational stiffness profile and decrease the twist stiffness. The twist stiffness fluctuates periodically with gear rotation generating fluctuating moments (shuttling) that can potentially excite vibrations.

Structured overlay for heterogeneous environments

Recent years have seen advances in building large Internet-scale index structures, generally known as structured overlays . Early structured overlays realized distributed hash tables (DHTs) which are ill suited for anything but exact queries. The need to support range queries necessitates systems that can handle uneven load distributions. However such systems suffer from practical problems—including poor latency, disproportionate bandwidth usage at participating peers, or unrealistic assumptions on peers' homogeneity, in terms of available storage or bandwidth resources. In this article we consider a system that is not only able to support uneven load distributions but also to operate in heterogeneous environments, where each peer can autonomously decide how much of its resources to contribute to the system. We provide the theoretical foundations of realizing such a network and present a newly proposed system Oscar based on these principles. Oscar can construct efficient overlays given arbitrary load distributions by employing a novel scalable network sampling technique. The simulations of our system validate the theory and evaluate Oscar's performance under typical challenges, encountered in real-life large-scale networked systems, including participant heterogeneity, faults, and skewed and dynamic load-distributions. Thus the Oscar distributed index fills in an important gap in the family of structured overlays, bringing into life a practical Internet-scale index, which can play a crucial role in enabling data-oriented applications distributed over wide-area networks.

Dynamic response of arch bridges traversed by high-speed trains

A mechanical model describing the planar elasto-dynamics of arch bridges with general arch profiles is presented. The model is amenable to analytical or semi-analytical treatments and is effective for parametric studies, design of control systems or structural optimizations. The Ritz's energy approach is employed to calculate the solutions of the vibration eigenvalue problem—natural frequencies and mode shapes—and the forced responses to external excitations, namely those induced by the passage of trains. A closed-form solution of the bridge dynamic response to the transit of trains with arbitrary load distributions and running speeds is found and the train-induced resonances are accordingly discussed. In particular, three European high-speed trains—the French TGV, the Italian ETR 500, and the German ICE—traversing a lower-deck steel arch bridge are considered and the ensuing responses are investigated.

Large deflection behavior and stability of slender bars under self weight

In this paper the buckling and post-buckling behavior of slender bars under self-weight are studied. In order to study the post-buckling behavior of the bar, a geometrically exact formulation for the non-linear analysis of uni-directional structural elements is presented, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled nonlinear equations which, together with the boundary conditions at the bar ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender bars under self-weight, including the influence of boundary conditions on the stability and large deflection behavior of the bar. In order to evaluate the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal bar. As this kind of structure presents a high index of slenderness, its answers could be affected by the introduction of conventional sensors. In this paper, an experimental methodology was developed, allowing the measurement of static or dynamic displacements without making contact with the structure, using digital image processing techniques. The proposed experimental procedure can be used to a wide class of problems involving large deflections and deformations. The experimental buckling and post-buckling behavior compared favorably with the theoretical and numerical results.

Arbitrary Load Distribution on a Layered Half Space

This paper develops a method which allows one to calculate the complete elastic field (stress field and displacements) of layered materials of transverse and complete isotropy under given load conditions. It is assumed that the layered body consists of an infinite half-space and various infinite planes which are all ideally bonded to each other. Thus, the interfaces are parallel to the surface of the resulting “coated half space.” The approach is based on the method of images in classical electrostatics. The final solution for an arbitrary load problem can be presented as a series of potential functions, where corresponding functions may be interpreted as “image loads” the analogous to “image charges.” The solution for the elastic field for any arbitrary stress distribution on the surface of the coated half space can be obtained in a relatively straightforward manner by using the method described here as long as the corresponding solution for the homogeneous half space is known. Further, if this solution of the homogeneous case may be expressed in terms of elementary functions, then the solution for the coated half space is elementary, too. Explicit formulas for the stress fields for some particular examples are given. [S0742-4787(00)01204-2]

Influence of geometric imperfections on the load capacity of orthotropic stiffened and composite shells of revolution with arbitrary meridians and boundary conditions

A stiffness matrix for an element of a shell of revolution has been derived, considering arbitrary load distributions and initial geometric imperfections. This element-stiffness matrix is based on the transfer-matrix method and describes the whole section of a shell of revolution between two rings in modal coordinates (a so-called super-element). The modal coordinates here are circumferential Fourier members, thus reducing the partial differential equations to ordinary ones. Several stability analyses investigating the sensitivity of composite shells to different geometric imperfection shapes were carried out. The influence of the load distribution and boundary conditions in combination with geometric imperfections was analysed by different modellings of a hypothetical Jupe Avant shell of the ARIANE 5 rocket.

Somewhat circular tensile cracks

In this paper we apply the method developed by Rice [1], of solving for the elastic field of a crack with a front perturbed from some reference shape, to solve the elasticity problems of somewhat circular planar tensile cracks under arbitrary load distributions. The method is based on a known solution for the stress intensity factor along a circular crack due to a pair of wedge-opening point forces on its surfaces. A full solution, accurate to first order in the deviation from a circular shape, is derived for the stress intensity factor and the crack opening displacement distributions. The results of a perturbation in a harmonic wave form suggest that a circular crack, under axially symmetric loading, can be configurationally unstable (not grow as a circle) for loadings that increase in intensity with distance from the center. Circular cracks with harmonic shape perturbations are found to have the same form of variation of the stress intensity factor with arc length along the crack edge (to first order accuracy) as found in previous work for a half plane crack. As a test case for the perturbation solution, an elliptical planar tensile crack under uniform tension is viewed as being perturbed from a circular crack. Results derived from the perturbation formulae through numerical evaluation are compared with the exact solutions existing in the literature. The perturbation results show a very good match with the exact solutions even when the semi-axis lengths of the elliptical crack differ by a factor of two (and by as much as a factor of three when special choices of the reference circular crack location are made). This suggests that the perturbation procedure presented here, while theoretically exact only to first order, can be used to produce acceptable results for some planar cracks whose shapes deviate appreciably from a circle.

Stress intensity factors for cracks at loaded holes-effect of load distribution

Stress intensity factors are evaluated for a radial crack at the edge of a circular hole subjected to a localized radial or tangential force on its perimeter. These factors can be used as Green's functions to determine the stress intensity factor when an arbitrary load distribution acts on the hole perimeter. Both the accuracy and ease-of-use of this Green's function technique are demonstrated by comparing some test cases with known results. The strong dependence of the stress intensity factor for short cracks upon the detailed load distribution on the perimeter of the hole is discussed, and the importance of fricitional forces is demonstrated in the determination of fatigue lifetimes in the presence of fretting

Continuous analysis of stresses from arbitrary surface loads on a half space

A new form of elemental surface load on a half space is introduced, presuming a quasi-pyramidal variation of load which is doubly linear in each of four rectangular parts of a surface rectangle. Approximations of arbitrary load distributions by sums of such elements are continuous, piecewise linear in two directions and well adaptable. The loads may be normal or tangential. The explicit solutions obtained for all stress and displacement components due to each elemental load involve only elementary functions, are free of the discontinuities which arise with stepwise elements, and are suitable for computing. Some illustrative stress distributions are presented for elemental loads and for multiple pyramidal loads involving both normal and tangential loads. The value of the load continuity in the more complicated analyses of surface cracks is also illustrated.

Vibration and acoustic radiation of elastically supported rectangular plates

A Green function solution is developed for the steady-state vibrations of an elastically supported rectangular plate coupled to a semi-infinite acoustic medium. Rotational motion at the plate boundaries is controlled by continuous distributions of rotary springs. The solution takes the form of that for a simply supported rectangular plate. The coefficients are determined from systems of simultaneous algebraic equations that include the coupling due to non-homogeneous boundary conditions and the acoustic surface impedance. The solution is also extended to cover the case of an arbitrary load distribution and an expression is derived for the power balance in the coupled plate-fluid system. Results of a numerical evaluation of the modal coupling factors due to fluid loading are compared with low frequency approximations. Effects of the support conditions on the low frequency sound radiation from a plate are illustrated by an example.

On a Green's function for plate bending.

T deflection of a uniformly loaded rectangular plate with one pair of parallel edges ridigly connected to two identical beams was considered by Smith and Pan. This brief note gives a series solution for the more general case of the deflection of a rectangular plate subjected to a concentrated load at an arbitrary location. The plate is uniform in cross section, simply supported along one pair of parallel edges, and rigidly attached to identical elastic beams along the other pair of parallel edges. To facilitate the solution, this problem is divided into a sy metric and a skew-symetric problem. The superposition of the resulting solutions yields the desired solution that can be used as a Green's function to determine the deflection of a plate with the same boundary conditions and subjected to an arbitrary load distribution. The partial differential equation for the problem considered here can be written as follows :

Stresses Produced in a Half Plane by Moving Loads

Abstract A study is made of stresses and displacements induced in an elastic half plane (plane strain) by a concentrated line load moving at a constant speed along its surface. The stress field for an arbitrary load distribution can be built up by superposition of these concentrated-load solutions. Three cases are considered: (a) The load is moving more slowly than either the longitudinal or transversal wave speeds of the elastic medium (subsonic case). (b) The load speed is between the two wave speeds (transonic case). (c) The load speed is greater than either wave speed (supersonic case). In each of these cases the nature of the singularity caused by the load is examined and the complete solution is given.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

Deflections of Circular Beams Resting on Elastic Foundations Obtained by Methods of Harmonic Analysis

Abstract Solutions in form of Fourier series are given for the problem of circular beams resting on elastic foundations on the assumption that the foundation reacts according to the classical Winkler-Zimmermann hypothesis. The case of an arbitrary load distribution is disposed of by separate treatment of the symmetric and antisymmetric load components. Numerical tables of the coefficients of the trigonometric series expressing deflections, angles of twist, bending and twisting moments are presented for both symmetric and antisymmetric loadings.