Volume 20 (2015): Issue 4 (December 2015)

A general numerical analysis theory capable of describing the behaviour of a non-uniform beam resting on variable one parameter (Winkler) foundation under a uniform partially distributed moving load is developed. The versatile numerical solution technique employed is based on the finite element and Newmark integration methods. The analysis is carried out in order to evaluate the effect of the following parameters (i) the speed of the moving load (ii) the span length of the beam (iii) two types of vibrating configurations of the beam (iv) the load’s length and (v) the elastic foundation modulus, on the dynamic behaviour of the non-uniform beam resting on the variable one-parameter foundation. Numerical examples which showed that the above parameters have significant effects on the dynamic behaviour of the moving load problem are presented.

The purpose of this paper is to study the two dimensional deformation due to an internal heat source in a thermoelastic microelongated solid. A mechanical force is applied along an overlaying elastic layer of thickness h. The normal mode analysis has been applied to obtain the exact expressions for the displacement component, force stress, temperature distribution and microelongation. The effect of the internal heat source on the displacement component, force stress, temperature distribution and microelongation has been depicted graphically for Green-Lindsay (GL) theory of thermoelasticity.

In the present study, we have developed a code using Matlab software for solving a rectangular aluminum plate having void, notch, at different boundary conditions discretizing a two dimensional (2D) heat conduction equation by the finite difference technique. We have solved a 2D mixed boundary heat conduction problem analytically using Fourier integrals (Deb Nath et al., 2006; 2007; 2007; Deb Nath and Ahmed, 2008; Deb Nath, 2008; Deb Nath and Afsar, 2009; Deb Nath and Ahmed, 2009; 2009; Deb Nath et al., 2010; Deb Nath, 2013) and the same problem is also solved using the present code developed by the finite difference technique (Ahmed et al., 2005; Deb Nath, 2002; Deb Nath et al., 2008; Ahmed and Deb Nath, 2009; Deb Nath et al., 2011; Mohiuddin et al., 2012). To verify the soundness of the present heat conduction code results using the finite difference method, the distribution of temperature at some sections of a 2D heated plate obtained by the analytical method is compared with those of the plate obtained by the present finite difference method. Interpolation technique is used as an example when the boundary of the plate does not pass through the discretized grid points of the plate. Sometimes hot and cold fluids are passed through rectangular channels in industries and many types of technical equipment. The distribution of temperature of plates including notches, slots with different temperature boundary conditions are studied. Transient heat transfer in several pure metallic plates is also studied to find out the required time to reach equilibrium temperature. So, this study will help find design parameters of such structures.

In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.

In order to estimate the inductive power set in the armature of the high-speed solenoid valve (HSV) during the open loop control (OLC) using pulse width modulation (PWM) an analytical explicit formula has been derived. The simplifications taken both in the geometry and in the physical behavior of the HSV were described. The inductive power was calculated for different boundary conditions and shown as a function of the frequency of the coil current. The power set in the armature was used as an input to the thermal calculation. The thermal calculation had an objective to estimate the time dependent temperature distribution in the armature of the HSV. All the derivation steps were presented and the influence of different boundary conditions was shown and discussed. The increase of the temperature during the heating with inductive power has been evaluated both in the core and on the side surface of the HSV.

An analysis has been provided to determine the transient velocity and steady state entropy generation in a microfluidic Couette flow influenced by electro-kinetic effect of charged nanoparticles. The equation for calculating the Couette flow velocity profile is derived for transient flow. The solutions for momentum and energy equations are used to get the exact solution for the dimensionless velocity ratio and dimensionless entropy generation number. The effects of the dimensionless entropy generation number, Bejan number, irreversibility ratio, entropy generation due to fluid friction and due to heat transfer on dimensionless time, relative channel height, Brinkman number, dimensionless temperature ratio, nanoparticle volume fraction are analyzed.

The article presents numerical simulations for the modelling of seismic impact on the structure of unique cantilever cablestayed structure with the application of two methods. The Response Spectrum method, in which a spectrum of the structure’s responses to an earthquake’s impact is generated, and the Accelerogram method, in which we generate dynamic load in the form of a diagram of the connection between acceleration and time for the actual readings during a real earthquake. Both methods have been presented for the El Centro earthquake spectrum. This unique application of a cantilever cablestayed structure in public buildings will allow to assess the safety of this kind of load-bearing system in areas of increased risk of seismic activity. Cantilever cablestayed structures have so far never been designed or analyzed on seismically active areas. Based on numerical simulation we determined the effect of stiffness of load-bearing lines on the increase of stresses and displacements at cable stays joint with the end of the cantilever part of a building.

The flow of a viscous incompressible fluid through a vertical channel in the presence of radiation immersed in a porous medium has been studied. Approximate solutions have been obtained for the velocity and temperature fields, shear stresses and rate of heat transfer using the perturbation technique. It is found that the primary velocity decreases with an increase in the radiation parameter as well as the Prandtl number for cooling of the plate. It is also found that with an increase in the permeability parameter, the primary velocity increases for cooling of the plate. The magnitude of the secondary velocity decreases near the plate y = 0 and increases near the plate y = d with an increase in the permeability parameter. The temperature distribution decreases with an increase of the radiation parameter as wall as the Prandtl number for cooling of the plate. The shear stresses and the rate of heat transfer, which are of physical interest, are presented in the form of tables.

A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.

This paper reports some results of turbulent boundary layer computation. The calculation is made assuming that law of the wall is valid throughout the boundary layer. Simple relations are proposed for friction for a smooth pipe and a flat plate at zero incidence. The results are compared with recent measurements. Encouraging results are obtained for both the cases of flows.

An unsteady two-dimensional stagnation-point mixed convection flow of a viscous, incompressible dusty fluid towards a vertical stretching sheet has been examined. The stretching velocity and the free stream velocity are assumed to vary linearly with the distance from the stagnation point. The problem is analyzed using similarity solutions. The similarity ordinary differential equations were then solved numerical by using the RKF-45 method. The effects of various physical parameters on the velocity profile and skin-friction coefficient are also discussed in this paper. Some important findings reported in this work reveal that the effect of radiation has a significant impact on controlling the rate of heat transfer in the boundary layer region.

The instability of plane interface between two superposed Rivlin-Ericksen elastico-viscous fluids saturated through a porous medium has been studied to include the suspended (dust) particles effect. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like Newtonian fluids. It found that for a potentially stable arrangement the Rivlin-Ericksen elastico-viscous fluid of different permeabilities in the presence of suspended particles in a porous medium is stable, whereas in a potentially unstable case instability of the system occurs. In the presence of a magnetic field for a potentially stable arrangement the system is always stable and for the potentially unstable arrangement, the magnetic field succeeds in stabilizing certain wave-number band which was unstable in the absence of the magnetic field.

Thermal barrier coatings (TBCs) are widely used on different hot components of gas turbine engines such as blades and vanes. Although, several mechanisms for the failure of the TBCs have been suggested, it is largely accepted that the durability of these coatings is primarily determined by the residual stresses that are developed during the thermal cycling. In the present study, the residual stress build-up in an electron beam physical vapour deposition (EB-PVD) based TBCs on a coupon during thermal cycling has been studied by varying three parameters such as the cooling rate, TBC thickness and substrate thickness. A two-dimensional thermomechanical generalized plane strain finite element simulations have been performed for thousand cycles. It was observed that these variations change the stress profile significantly and the stress severity factor increases non-linearly. Overall, the predictions of the model agree with reported experimental results and help in predicting the failure mechanisms.

The paper contains two parts. In the first part, basic relationships were derived and some problems connected with stability loss during hydraulic forming of round metallic drawpieces with liquid pressure were discussed. The aim of the considerations is to test drawability of sheets by estimation of acceptable values of plastic strains and the corresponding heights of spherical shells. The analysis was based on some selected real conditions of stability loss. The influence of the coefficient of material hardening for the drawpiece, the coefficient of normal anisotropy and coefficients of plane anisotropy on acceptable values of plastic strains and heights of the formed drawpieces corresponding to the given condition of stability loss was also tested.

Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.