A thorough investigation of the interdependent behavior of prestressed system

Due to the existing of many prestressed members in the structural system, the interdependent behavior of all prestressed members is the main concern in the analysis of the pretension process. A thorough investigation of this mutual effect is essential for an effective, reliable, and optimal analysis. Focus on this aspect, this paper presents an investigation of the interdependent behavior of all prestressed members in the whole structural system based on influence matrix (IFM). Four different types of IFM are introduced. Two different solving methods are brought forth to analyze the pretension process. The direct solving method solves for the accurate solution, whereas the iterative solving method repeatedly amends to achieve an approximate solution. A numerical example is then conducted. The result shows that various kinds of complicated batched and repeated tensioning schemes can be analyzed reliably, effectively, and completely based on IFM.

Singularity-free path planning for the Stewart platform manipulator

This paper addresses the problem of singularity-free path planning for the six-degree-of-freedom parallel manipulator known as the Stewart platform manipulator. Unlike serial manipulators, the Stewart platform possesses singular configurations within the workspace where the manipulator is uncontrollable. An algorithm has been developed to construct continuous paths within the workspace of the manipulator by avoiding singularities and ill-conditioning. Given two end-poses of the manipulator, the algorithm finds out safe (well-conditioned) via points and plans a continuous path from the initial pose to the final one. When the two end-poses belong to different branches and no singularity-free path is possible, the algorithm indicates the impossibility of a valid path. A numerical example has also been presented as illustration of the path planning strategy.

Certain Aspects Related To Computation By Modified Crack Closure Integral(MCCI)

This paper presents the proper computational approach for the estimation of strain energy release rates by modified crack closure integral (MCCI). In particular, in the estimation of consistent nodal force vectors used in the MCCI expressions for quarter-point singular elements (wherein all the nodal force vectors participate in computation of strain energy release rates by MCCI). The numerical example of a centre crack tension specimen under uniform loading is presented to illustrate the approach.

Response And Stability Of A Stochastic Beam-Column Using Stochastic Fem

A beam-column resting on continuous Winkler foundation and discrete elastic supports is considered. The beam-column is of variable cross-section and the variation of sectional properties along the axis of the beam-column is deterministic. Young's modulus, mass per unit length and distributed axial loadings of the beam-column have a stochastic distribution. The foundation stiffness coefficient of the Winkler model, the stiffnesses of discrete elastic supports, stiffnesses of end springs and the end thrust, are all considered as random parameters. The material property fluctuations and distributed axial loadings are considered to constitute independent, one-dimension uni-variate homogeneous real stochastic fields in space. The foundation stiffness coefficient, stiffnesses of the discrete elastic supports, stiffnesses of end springs and the end thrust are considered to constitute independent random variables. Static response, free vibration and stability behaviour of the beam-column are studied. Hamilton's principle is used to formulate the problem using stochastic FEM. Sensitivity vectors of the response and stability parameters are evaluated. Using these statistics of free vibration frequencies, mode shapes, buckling parameters, etc., are evaluated. A numerical example is given.

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

Vibrations of laminated beams

Governing equations in the form of simultaneous ordinary differential equations have been derived for natural vibration analysis of isotropic laminated beams. This formulation includes significant secondary effects such as transverse shear and rotatory inetia. Through a numerical example, the influence of these secondary effects has been studied.

A time minimising transportation problem with quality dependent time

The usual assumption made in time minimising transportation problem is that the time for transporting a positive amount in a route is independent of the actual amount transported in that route. In this paper we make a more general and natural assumption that the time depends on the actual amount transported. We assume that the time function for each route is an increasing piecewise constant function. Four algorithms - (1) a threshold algorithm, (2) an upper bounding technique, (3) a primal dual approach, and (4) a branch and bound algorithm - are presented to solve the given problem. A method is also given to compute the minimum bottle-neck shipment corresponding to the optimal time. A numerical example is solved illustrating the algorithms presented in this paper.

Optimal maintenance and replacement via a semi-Markov decision model

Optimal bang-coast maintenance policies for a machine, subject to failure, are considered. The approach utilizes a semi-Markov model for the system. A simplified model for modifying the probability of machine failure with maintenance is employed. A numerical example is presented to illustrate the procedure and results.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Measuring tax efficiency: A tax optimality index

This paper introduces an index of tax optimality that measures the distance of some current tax structure from the optimal tax structure in the presence of public goods. This index is defined on the [0, 1] interval and measures the proportion of the optimal tax rates that will achieve the same welfare outcome as some arbitrarily given initial tax structure. We call this number the Tax Optimality Index. We also show how the basic methodology can be altered to derive a revenue equivalent uniform tax, which measures the tax burden implied by the public sector. A numerical example is used to illustrate the method developed, and extensions of the analysis to handle models with multiple households and nonlinear taxation structures are undertaken.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Information Theoretic Results for Three-User Cognitive Channels

In this paper, we introduce the three-user cognitive radio channels with asymmetric transmitter cooperation, and derive achievable rate regions under several scenarios depending on the type of cooperation and decoding capability at the receivers. Two of the most natural cooperation mechanisms for the three-user channel are considered here: cumulative message sharing (CMS) and primary-only message sharing (PMS). In addition to the message sharing mechanism, the achievable rate region is critically dependent on the decoding capability at the receivers. Here, we consider two scenarios for the decoding capability, and derive an achievable rate region for each one of them by employing a combination of superposition and Gel'fand-Pinsker coding techniques. Finally, to provide a numerical example, we consider the Gaussian channel model to plot the rate regions. In terms of achievable rates, CMS turns out to be a better scheme than PMS. However, the practical aspects of implementing such message-sharing schemes remain to be investigated.