Buckling of a Timoshenko beam on elastic foundation with uncertain input data

A monotone dependence of the critical buckling load of a simplysupported Timoshenko–Mindlin beam both on the shear correctionfactor and on the stiffness of foundation is proved. Then theworst-scenario method is employed to find the ‘most dangerous’input data.     

On a structural acoustic model with interface a Reissner-Mindlin plate or a Timoshenko beam

This paper is concerned with a model which describes the interaction of sound and elastic waves in a structural acoustic chamber in which one “wall” is flexible and flat. The model is new in the sense that the composite dynamics of the three-dimensional structure is described by the linearized equations for a gas defined on the interior of the chamber and the Reissner-Mindlin plate equations on the two-dimensional flat wall of the chamber, while, if a two-dimensional acoustic chamber is considered, the Timoshenko beam equations describe the deflections of the one-dimensional “wall.” With a view to achieving uniform stabilization of the structure linear feedback boundary damping is incorporated in the model, viz. in the wave equation for the gas and in the system of equations for the vibrations of the elastic medium. We present the uniform stability result for the case of a two-dimensional chamber and outline the method for the three-dimensional model which shows strong resemblance with the system of dynamic plane elasticity.     

On the American option‐pricing model with an uncertain volatility

In this paper, we study an American option‐pricing model with an uncertain volatility. Some properties for the option price are derived. Particularly, a global spread for the option price is proved when the volatility depends on the underlying security and time. This result confirms the observed fact from the real financial data in option markets. Copyright © 2015 John Wiley & Sons, Ltd.     

Existence of the displacements field for an elasto-plastic body subject to Hencky's law and Von Mises yield condition

We give necessary and sufficient conditions on body and traction forces for the existence of the displacements field for an elasto-plastic body subject to Hencky's law and Von Mises yield condition.     

A strip yield model solution for an internally cracked piezoelectric strip

An analysis of the crack closure and fatigue crack growth rate have been carried out for an infinitely long poled piezoelectric ceramic strip weakened by a straight hair line internal crack. The ceramic under consideration is assumed to be mechanically more brittle. The crack faces are perpendicular to the poled direction of the strip. The crack faces open in Mode-I deformation on account of in-plane tension applied to the edges of the strip together with either an in-plane electric displacement prescribed on edges of the strip or a uniform constant electric field prescribed on its edges. As a result, a yield zone is formed ahead of each tip of the crack. The yield zones developed are then arrested by applying a normal, cohesive, linearly varying yield point-stress to their rims. For each case, the Fourier transform method is used to find a solution. The resulting integral equations are solved numerically. Expressions are derived for the crack opening displacement and the crack growth rate. The variations in these quantities are plotted in relation to the affecting parameters, viz., the strip thickness, the yield zone length, the electric displacement, and material constants. A case study is presented graphically for PZT-4, PZT-5H, and BaTiO₃ ceramics. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 647–664, September–October, 2008.     

Uniform stabilization of a nonlinear structural acoustic model with a Timoshenko beam interface

This paper is concerned with a nonlinear model which describes the interaction of sound and elastic waves in a two‐dimensional acoustic chamber in which one flat ‘wall’, the interface, is flexible. The composite dynamics of the structural acoustic model is described by the linearized equations for a gas defined on the interior of the chamber and the nonlinear Timoshenko beam equations on the interface. Uniform stability of the energy associated with the interactive system of partial differential equations is achieved by incorporating a nonlinear feedback boundary damping scheme in the equations for the gas and the beam. Copyright © 2006 John Wiley & Sons, Ltd.     

Existence of positive periodic solution for the electron beam focusing system

In this paper, we study the mathematical model of electron beam focusing system where a>0,b?0 are constants, find conditions for the existence of positive π‐periodic solution of the above equation by using analytical method and comparison theory, and prove the existence of positive π‐periodic solution by the continuously dependent theory of initial value problem. Copyright © 2004 John Wiley & Sons, Ltd.     

Energy decay of solutions for an extensible beam equation with a weak nonlinear dissipation

In this paper, we study the decay property of the solutions to an extensible beam equation with a weak nonlinear dissipation. We establish an explicit and general decay result, depending on nonlinear function g and positive function σ, using some properties of convex functions. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of a robust tracker and disturbance attenuator for uncertain systems with time delays

This article considers the composite nonlinear feedback control method for robust tracker and disturbance attenuator design of uncertain systems with time delays. The proposed robust tracker improves the transient performance and steady state accuracy simultaneously. The asymptotic robust tracking conditions are provided in the form of linear matrix inequalities and the resultant conditions yield the controller gains. Moreover, to improve the reference tracking performance, a new nonlinear function for the composite feedback control law is offered. Simulation results are presented to verify the theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 340–348, 2015     

Mathematical solution for bending of short hybrid composite beams with variable fibers spacing

In this study, the static response is presented for a simply supported functionally graded hybrid beam subjected to a transverse uniform load. Material properties of the beam are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. By varying the fiber volume fraction within a symmetric laminated beam and combining two fiber types to create a hybrid functionally graded material (FGM) can offer desirable increases in axial and bending stiffness. The equations governing the hybrid FGM beams are determined using the principle of virtual work (PVW) arising from the higher order shear deformation theories. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick hybrid FGM beam under uniform distributed load are discussed in depth. The effect of power-law exponent on the deflection and stresses are also commented.     

A mini max theorem for the quasi-convex functional and the solution of the nonlinear beam equation

In this paper, a definition of a kind of quasi-convex functional was proposed and two properties of the quasi-convex functional were proved. A mini max theorem due to Stepan A. Tersian was generalized by using the properties of the quasi-convex functional. The existence and uniqueness of solution of the boundary value problem for the nonlinear beam equation was probed and an existence and uniqueness theorem was presented.     

Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model

Sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive Lasota-Wazewska model for the survival of red blood cells.     

Moments for a multivariate linear model with an application to the growth curve model

An extended growth curve model is considered which, among other things, is useful when linear restrictions exist on the mean in the ordinary growth curve model. The maximum likelihood estimators consist of complicated stochastic expressions. It is shown how, by the aid of fairly elementary calculations, the dispersion matrix for the estimator of the mean and the expectation of the estimated dispersion matrix are obtained. Results for Wishart, inverted Wishart, and inverse beta variables are utilized. Additionally, some asymptotic results are presented.     

Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty

This paper is concerned with the comparison of two non-probabilistic set-theoretical models for dynamic response measures of an infinitely long beam. The beam is on an uncertain foundation and subjected to a moving force with constant speed. The steady state vibration is analyzed with finite element method. The dynamic responses of the beam are approximated to the first-order respect of the uncertainty variables. As a rule, in convex models and interval analysis, the uncertainties are considered to be unknown, but they give out their allowable vector space. Comparing the convex models with interval analysis in mathematical proofs and numerical calculations, it’s shows that under the condition of transform an interval vector to an outer enclosed ellipsoid, the dynamic response of the infinitely long beam predicted by interval analysis is smaller than that by convex models; under the condition of transform a hyperellipsoid to an outer enclosed interval vector, the dynamic response of the infinitely long beam calculated by convex models is smaller than that by interval analysis method.     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

A robust optimization model for a cross-border logistics problem with fleet composition in an uncertain environment

Since the implementation of the open-door policy in China, many Hong Kong-based manufacturers' production lines have moved to China to take advantage of the lower production cost, lower wages, and lower rental costs, and thus, the finished products must be transported from China to Hong Kong. It has been discovered that logistics management often encounters uncertainty and noisy data. In this paper, a robust optimization model is proposed to solve a cross-border logistics problem in an environment of uncertainty. By adjusting penalty parameters, decision-makers can determine an optimal long-term transportation strategy, including the optimal delivery routes and the optimal vehicle fleet composition to minimize total expenditure under different economic growth scenarios. We demonstrate the robustness and effectiveness of our model using the example of a Hong Kong-based manufacturing company. The analysis of the trade-off between model robustness and solution robustness is also presented.     

Ruin problems for an autoregressive risk model with dependent rates of interest

In this paper, we consider a discrete insurance risk model in which the claims, the premiums and the rates of interest are assumed to have dependent autoregressive structures (AR(1)). We derive recursive and integral equations for expected discounted penalty function. By these equations, we obtain generalized Lundberg inequality for the infinite time severity of ruin and hence for the infinite time ruin probability, consider asymptotic formula for the finite time ruin probability when loss distributions have regularly varying tails, and study some probability properties of the duration of ruin.     

The simplified solution algorithm for an integrated supplier-buyer inventory model with two-part trade credit in a supply chain system

Ho et al. [Ho, C.H., Ouyang, L.Y., Su, C.H., 2008. Optimal pricing, shipment and payment policy for an integrated supplier-buyer inventory model with two-part trade credit, European Journal of Operational Research 187, 496-510] discussed the integrated inventory model with two-part trade credit and presented an algorithm to solve it. Basically, Ho et al.’s inventory model is correct and interesting. However, this paper indicates that the solution algorithm described in Ho et al. (2008) can be simplified further. So, this paper can not only derive the optimally closed-form formulations for the optimal numbers of shipments but also develop different algorithms to improve those in Ho et al. (2008). Numerical examples illustrate that the algorithm to locate the optimal solution is rather accurate and rapid.     

Spline estimators for semi-functional linear model

In this paper, we introduce a semi-functional linear model in which a scalar response variable is explained by a linear operator of a random function and a nonparametric function of a real-valued random variable. We study the spline estimators of the functional coefficient and nonparametric function and obtain the rates of convergence of the spline estimators. Finally, we present some simulation results that illustrate the performance of our estimation method.