The paper presents a method for modelling material non-linearity for use in the analysis of load-carrying capacity and deformations of reinforced concrete beams, columns and membrane-bending plates subjected to long-term loads. Physical relationships expressing relations between internal forces and stresses, strains and stiffness are derived on the basis of the fracture and creep theories for concrete and using non-linear stress-strain diagrams modified for time effects. A specific implementation technique of a genetic algorithm is developed to find multiple solutions to non-smooth problems under consideration.
    The computation technique proposed is found to be effective in numerical examples, and an adequate accuracy of the analysis is verified by comparison with experimental data.

     This paper presents a numerical study of a fully developed laminar flow of a non-Newtonian fluid in a helical pipe. An orthogonal helical coordinate system is utilized and the Navier-Stokes equations for the non-Newtonian fluid in this coordinate system are derived. The SIMPLE algorithm with a staggered grid is adopted to solve the governing equations. The effects of the pressure gradient, the curvature, and the torsion on the fully developed laminar flow in helical pipes are investigated. The comparison of flow dynamics between Newtonian and non-Newtonian fluids is presented.

     The helical flow of a Casson fluid between infinitely long coaxial cylinders is analyzed, when the inner cylinder has a given constant angular velocity, and a constant axial flow rate is imposed. Perturbation methods are applied in two circumstances of physical interest - that of low axial flow rates; and that of small intercylindrical gap width - to yield approximate expressions describing the fluid velocity field; and the Reiner-Riwlin equation, the fundamental relationship linking the angular velocity of the inner cylinder, the torque experienced there, and the given axial flow rate. The accuracy of these expressions is tested by comparison with solutions generated using numerical computation.

     In this article it has been sought to study the effect of transverse roughness on the behaviour of slider bearings with squeeze film formed by a magnetic fluid. The roughness of the bearing surface is modelled by a stochastic random variable with non zero mean, variance and skewness. The associated Reynolds' equation is stochastically averaged with respect to the random roughness parameter. Results for bearing performance characteristics such as load carrying capacity, center of pressure, frictional force and coefficient of friction for different values of mean, standard deviation and measure of symmetry are numerically computed. In order to decipher the quantitative effect of roughness on the performance characteristics four different shapes namely; plane slider, exponential slider, hyperbolic slider and secant slider for the lubricant film are considered. The results are presented graphically. It is noticed that the bearing suffers on account of transverse surface roughness. The results show that the use of a magnetic fluid as lubricant increases the load carrying capacity, decreases the coefficient of friction and affects the center of pressure marginally. It is further observed that the effect of magnetization on the plane and secant shaped bearings is nominal while the effect on exponential and hyperbolic slider bearing is significant. In addition it is easily seen that by increasing the strength of the magnetic field the adverse impact on the bearing due to roughness can be minimized.

     A boundary layer analysis is presented to study the effects of thermal dispersion of a non-Newtonian fluid on non-Darcy axisymmetric free convection over a horizontal surface embedded in a porous medium. The Ostwald-de-Waele power-law model is used to characterize the non-Newtonian fluid behavior. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. Similarity solutions are obtained when the surface temperature varies as the square root of the radial distance (i.e., the prescribed temperature PT) or when heat flux is constant (i.e., the prescribed heat flux PHF). The effects of the dispersion and non-Darcy parameters as well as the power-law index n on the velocity, temperature, the Nusselt number and the boundary layer thickness are shown on graphs. The numerical values of the rate of heat transfer through the boundary layer in terms of the Nusselt number are entered in a table.

     An analysis is presented to investigate the flow and heat transfer characteristic of a viscous incompressible and electrically conducting fluid through a porous medium bounded by two long vertical parallel plates in the presence of a uniform magnetic field applied transversely to the flow. The governing momentum and energy equations are solved by the Laplace transform technique and the solutions are presented for velocity and temperature distributions and shear stress. The effects of the four parameters, namely, the Darcy number, viscosity ratio parameter, magnetic Hartmann number, and Prandtl number on temperature and velocity distributions are shown in graphs and presented through the results and discussion. Also, the effects of these four parameters on skin friction are given.

     The steady state response at viscous fluid/micropolar elastic solid interface to a moving point load has been studied for subsonic, supersonic and transonic load velocities. The Fourier transform has been used to solve the problem. The displacement, microrotation and stress components for a micropolar elastic solid so obtained in the physical domain are computed numerically by using the numerical inversion technique. Viscosity and micropolarity effects on the resulting expressions have been presented graphically for a specific material.

     The analytic expressions for the displacements, microrotation, stresses and volume fraction field on the free surface of a micropolar elastic half-space with voids as a result of moving an inclined load have been obtained. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The problem has been solved by employing the Eigen-value approach after using the Fourier transform as the use of matrix notation avoids unwidely mathematical expressions. The technique used in the present paper is simple, straightforward and convenient for numerical computations. The variations of the displacements, stresses and volume fraction field with the horizontal distance have been shown graphically for a particular model. A special case has also been discussed.

     The instability of streaming Walters B' elastico-viscous fluids in hydromagnetics through porous medium is considered. The case of two uniform streaming fluids separated by a common horizontal interface is considered. It is found that for the special case when perturbations in the direction of streaming are ignored, the system can be stable or unstable, depending upon kinematic viscoelasticity, medium porosity and medium permeability, for both potentially unstable and stable configurations. In all other directions, a minimum value of wave-number has been found and the system is unstable for all wave-numbers greater than this minimum wave number and the instability of the system is found to be postponed due to the presence of the magnetic field.

     The aim of the present problem is to investigate the efficiency of the method of Adomian for the solution of non-linear and complicated differential equation in a random medium. Here the problem is connected with the investigation of the mean and variance of the displacement distribution in a thin linear random non-homogeneous Biot type viscoelastic semi-infinite rod, due to general time-dependent displacement input at the rod. A truncated series solution of the wave problem following the method of Adomian after using the Laplace transform is obtained for small random variations in viscoelastic properties. Three specific cases concerning the probability measure as a function of the continuous type of random variable have been discussed.

     The two-dimensional steady incompressible flow past an impermeable sphere embedded in a porous medium is studied analytically using the Brinkmann model- specifying a uniform shear away from the sphere. A closed form solution is obtained for the governing equations. It is found that the increase in the permeability of a porous medium and viscosity ratio is to increase the thickness of the Brinkman boundary layer. The analysis is also concerned with the explanation of the velocity overshoot behavior. The effects of shear stress and the separation parameter are also discussed. The streamlines are drawn for different values of the porous parameter and the viscosity ratio and some important conclusions are drawn.

     In this note, the unsteady flow of a Maxwell fluid produced by non-coaxial rotation while a disk and the fluid at infinity are initially rotating with the same angular velocity about a common axis is considered. Even in the case of a non-Newtonian fluid, it is shown that there is an exact solution for this flow geometry. The velocity field is obtained with the help of the Laplace transform technique.