The failure of frames

It has been seen that the number of users in (web server) are increasing every now and then. This results in bottleneck which may lead to crashing of web servers or reduces the quality of service. So, there is a need of efficient and robust algorithm for load balancing. We have proposed an algorithm that gives better result and is capable of balancing the load on data centre subjected to the key feature. As Load balancing is the critical task in the technical era and the traffic in the web is increasing exponentially, we propose a solution which deals with core load balancing to resolve this trending issue. Here we have designed an intelligent sensing algorithm that will help the server to distribute the load according to the availability of server, location and then redirect the request to comparatively most available server. Distribution of load is done according to the availability of the system instead of round robin fashion. Availability of a server is computed according to current trifle load, current critical load and a deviation value. Depending upon the computed load: the most available, available and least available server are found. Finally, the request is dispatched to the nearest server which is highly available.

A numerical method for the topological design of periodic continuous domains under general loading is presented. Both the analysis and the design are defined over a single cell. Confining the analysis to the repetitive unit is obtained by the representative cell method which by means of the discrete Fourier transform reduces the original problem to a boundary value problem defined over one module, the representative cell. The repeating module is then meshed into a dense grid of finite elements and solved by finite element analysis. The technique is combined with topology optimization of infinite spatially periodic structures under arbitrary static loading. Minimum compliance structures under a constant volume of material are obtained by using the densities of material as design variables and by satisfying a classical optimality criterion which is generalized to encompass periodic structures. The method is illustrated with the design of an infinite strip possessing 1D translational symmetry and a cyclic structure under a tangential point force. A parametric study presents the evolution of the solution as a function of the aspect ratio of the representative cell.

This paper assesses the applicability of bearing capacity theory for evaluating the forces generated on wheels operating on clay under steady rolling conditions. Considering advances in bearing capacity theory, in particular the interaction diagrams developed for general loading, a theoretical model for computing the horizontal force or torque from fundamental input parameters such as the vertical force (weight), wheel diameter, and undrained shear strength of the soil is presented. The predictions are compared with existing analytical solutions and data from laboratory testing, and reasonable agreement is demonstrated. The newly proposed model provides a means to predict wheel forces analytically under any operating condition (driven, braked, or towed), provided the contact length and so-called contact angle, which defines the position of the contact interface, can be estimated. The model provides a rigorous, convenient framework for evaluating wheel forces under arbitrary loading and enables a natural physical interpretation of the mobility problem.

This paper presents application of fuzzy set theory and interval arithmetic for computing the branch currents, node voltages. First load currents at every node are estimated based on hourly load pattern of different types of consumers using fuzzy set theory. Once the fuzzy load currents at each node are estimated, then by using forward path information matrix the branch currents are computed using the concepts of arithmetic operations on closed intervals. Node voltages are computed using the simple relationship of sending end and receiving end voltages and using the concept of arithmetic operations on closed intervals. The effectiveness of the proposed method is demonstrated through an example. It is also compared with the general load estimation process.

Crack energy density of a piezoelectric material under general electromechanical loading

The bifilar pendulum is often used for indirect measurements of mass moments of inertia of bodies that possess complex geometries. The exact equation of motion of the bifilar pendulum is highly nonlinear, and has not been solved in terms of elementary functions. Extensive use has been made, however, of the linearized approximation to the exact equation, and it has been assumed that the simple harmonic oscillator adequately describes the motion of the bifilar pendulum. It is shown here that such is generally not the case. Numerical solutions to the exact nonlinear differential equations of motion are obtained for a range of values of initial angular displacement, filament length, and radius of gyration. The filament length and the radius of gyration are normalized with respect to the half-spacing between the filaments. It is shown that the approximate solution gives good results only for small ranges of the system parameters.

The problem of a circular plate, with a central hole, elastically constrained against rotation and deflection, acted upon by a transverse linear temperature gradient or a general axisymmetrical loading condition is considered in this paper. With the aid of presented graphs and simple algebraic equations, it is a relatively simple matter to construct the desired deflection and stress pattern for any combination of elastic constraints and load distribution.

Young’s modulus and Poisson ratio are essential parameters for rock brittleness evaluation. At present, prestack inversions of these parameters mostly adopt linear approximation, whereas the nonlinear inversion methods that are based on the exact Zoeppritz equation are seldomly conducted. Nevertheless, in the case of large incident angles and high-impedance contrast, the nonlinear equation has higher accuracy than the linear approximation. It is more in line with the nature of geophysical inversion problems, and it describes the variation of formations’ elastic parameters better than the linear approximation does. Therefore, based on the exact solution of the Zoeppritz equation, we have parameterized and derived a new nonlinear reflection coefficient equation using nonlinear Young’s modulus, Poisson ratio, and density (YPD) as variables. Subsequently, by combining the inverse operator algorithm with the YPD equation, we develop a new nonlinear amplitude-variation-with-offset inversion scheme. This approach can robustly extract Young’s modulus and Poisson ratio from seismic data and identify shale-gas sweet spot locations within the reservoir, as well as predict reservoir fluid properties. We have tested the accuracy and applicability of this approach with synthetic and real data examples.

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Summary The exact Zoeppritz equations have been simplified to involve non-linear contributions from the elastic rock property contrasts. This approximation is more accurate than the linearized equation widely used by the industry. The non-linear equations are a result of expanding the exact equations to second order in the rock property contrasts. Consistent with the original linearizations provided by Bortfeld and others, no explicit small angle assumptions have been made using the ray parameter p or other small angle related parameters. The resulting equations are more accurate than the linearized equations, especially for large rock property contrasts and large angles of incidence. Inversion, based upon these non-linear equations, provides more accurate and stable results and allows amplitudes corresponding to very large angles found in modern long cable acquisition to be used in inversion. A number of examples illustrating the improved accuracy of these equations compared with the traditional linear equations will be provided. A number of examples of inversions, using the non-linear equations applied to both synthetic and real data, will also be provided.

Non-prismatic beams are widely employed in several engineering fields, e.g., wind turbines, rotor blades, aircraft wings, and arched bridges. While analytical solutions for variable cross-section beams are desirable, a model describing all stress components for beams with general variation of their cross-section under generalised loading remains an open and important problem to solve. To partly address this issue, we propose an analytical solution for stress recovery of untwisted, asymmetric, non-prismatic beams with smooth and continuous taper shape under general loading, considering plane stress conditions for isotropic materials undergoing small strains. The methodology follows Jourawski’s formulation, including the effect of asymmetric variable cross-section, with internal forces as known variables. We confirm the non-triviality of the stress field of non-prismatic beams, i.e., the dependency on all internal forces and beam geometry to shear and transverse stress distributions. As a particular novelty, the new formulation for transverse direct stress includes internal forces derivatives, resulting in greater accuracy than state-of-the-art models for distributed loading conditions. Also, closed-form solutions are introduced for non-prismatic and linearly tapered, generally asymmetric beams, both with rectangular cross-sections. For validation purposes, we consider three different practical beam models: a symmetric and an asymmetric, both linearly tapered, and an arched beam. The results, checked against commercial finite element analysis, show that the proposed model predicts the stress-field of non-prismatic beams under distributed loads with good levels of accuracy. Traction-free boundary condition requirements are naturally satisfied on the beam surfaces.

59 - Exact Second Order Equations

A new method for the static analysis of guyed towers has been developed. The tower and guy cables may be loaded by arbitrary distributed or concentrated forces, or both, and there are no a priori assumptions about cable shape (such as the usual catenary assumption). Effect of axial forces as well as shear deformation in the tower are taken into account. The base of the tower may be in any support condition between clamped and hinged including either extreme. Cables are handled by the Method of Imaginary Reactions. For the tower, integration algorithms for the nonlinear beam-column equations are demonstrated by comparison with the exact solution for the classical problem of the Elastica. The technique is then applied to a two-dimensional demonstration problem of a guyed tower. Extension to three dimensions is straightforward and will be reported later.

A method for the closed-form evaluation of critical buckling loads for planar strongly curved bars

Second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is obtained by using the cumulant expansion ensemble averaging method and by taking the time dependent sure part of the multiplicative operator into account. It is shown that the satisfaction of the commutativity and the reversibility requirements proposed earlier for linear stochastic differential equations without forcing are necessary for the linear stochastic differential equations with forcing when the cumulant expansion ensemble averaging method is used. It is shown that the applicability of the operator equality, which is used for the separation of operators in the literature, is also subjected to the satisfaction of the commutativity and the reversibility requirements. The van Kampen’s lemma, which is proposed for the analysis of nonlinear stochastic differential equations, is modified in order to make the probability density function obtained through the lemma depend on the forcing terms too. The second-order exact ensemble averaged equation for linear stochastic differential equations with multiplicative randomness and random forcing is also obtained by using the modified van Kampen’s lemma in order to validate the correctness of the modified lemma. Second-order exact ensemble averaged equation for one dimensional convection diffusion equation with reaction and source is obtained by using the cumulant expansion ensemble averaging method. It is shown that the van Kampen’s lemma can yield the cumulant expansion ensemble averaging result for linear stochastic differential equations when the lemma is applied to the interaction representation of the governing differential equation. It is found that the ensemble averaged equations given for one the dimensional convection diffusion equation with reaction and source in the literature obtained by applying the lemma to the original differential equation are restricted with small sure part of multiplicative operator. Second-order exact differential equations for the evolution of the probability density function for the one dimensional convection diffusion equation with reaction and source and one dimensional nonlinear overland flow equation with source are obtained by using the modified van Kampen’s lemma. The equation for the evolution of the probability density function for one dimensional nonlinear overland flow equation with source given in the literature is found to be not second-order exact. It is found that the differential equations for the evolution of the probability density functions for various hydrological processes given in the literature are not second-order exact. The significance of the new terms found due to the second-order exact ensemble averaging performed on the one dimensional convection diffusion equation with reaction and source and during the application of the van Kampen’s lemma to the one dimensional nonlinear overland flow equation with source is investigated.