An alternate form of the ramberg-osgood formula for matrix displacement analysis

A new stress-strain law, which is a three parameter representation of stress in terms of strain has been proposed for the matrix displacement analysis of structures made of non-hookean materials. This formula has been utilized to study three typical problems. These studies brought out the effectiveness and suitability of this law for matrix displacement analysis.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

Resistometric studies of solute-vacancy interactions and clustering kinetics in an FCC matrix [AlZn Alloy with Ag, Ce, Dy, Li, Nb, Pt, Sb, Y, or Yb]

Al-4.4 a/oZn and Al-4.4 a/oZn with Ag, Ce, Dy, Li, Nb, Pt, Y, or Yb, alloys have been investigated by resistometry with a view to study the solute-vacancy interactions and clustering kinetics in these alloys. Solute-vacancy binding energies have been evaluated for all these elements by making use of appropriate methods of evaluation. Ag and Dy additions yield some interesting results and these have been discussed in the thesis. Solute-vacancy binding energy values obtained here have been compared with other available values and discussed. A study of the type of interaction between vacancies and solute atoms indicates that the valency effect is more predominant than the elastic effect.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

Effect of matrix cracking and material uncertainty on composite plates

A laminated composite plate model based on first order shear deformation theory is implemented using the finite element method.Matrix cracks are introduced into the finite element model by considering changes in the A, B and D matrices of composites. The effects of different boundary conditions, laminate types and ply angles on the behavior of composite plates with matrix cracks are studied.Finally, the effect of material property uncertainty, which is important for composite material on the composite plate, is investigated using Monte Carlo simulations. Probabilistic estimates of damage detection reliability in composite plates are made for static and dynamic measurements. It is found that the effect of uncertainty must be considered for accurate damage detection in composite structures. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms. (C) 2010 Elsevier Ltd. All rights reserved.

Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.

Equivalence conditions for classes of linear and non-linear distributed parameter systems

Equivalence of certain classes of second-order non-linear distributed parameter systems and corresponding linear third-order systems is established through a differential transformation technique. As linear systems are amenable to analysis through existing techniques, this study is expected to offer a method of tackling certain classes of non-linear problems which may otherwise prove to be formidable in nature.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria