Thin film flow over a non-linear stretching sheet in presence of uniform transverse magnetic field

A thin viscous liquid film flow is developed over a stretching sheet under different non-linear stretching velocities in presence of uniform transverse magnetic field. Evolution equation for the film thickness is derived using long-wave approximation of thin liquid film and is solved numerically by using the Newton–Kantorovich method. It is observed that all types of stretching produces film thinning, but non-monotonic stretching produces faster thinning at small distance from the origin. Effect of the transverse magnetic field is to slow down the film thinning process. Observed flow behavior is explained physically.     

A Hybrid Particle Swarm Optimization Algorithm for the Redundancy Allocation Problem

The Redundancy Allocation Problem generally involves the selection of components with multiple choices and redundancy levels that produce maximum system reliability given various system level constraints as cost and weight. In this paper we investigate the series–parallel redundant reliability problems, when a mixing of components was considered. In this type of problem both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximise the reliability of system. A hybrid algorithm is based on particle swarm optimization and local search algorithm. In addition, we propose an adaptive penalty function which encourages our algorithm to explore within the feasible region and near feasible region, and discourage search beyond that threshold. The effectiveness of our proposed hybrid PSO algorithm is proved on numerous variations of three different problems and compared to Tabu Search and Multiple Weighted Objectives solutions.     

Malmquist indexes with quasi-fixed inputs: an application to school districts in Québec

We present a space and time allocation problem that arises in assembly halls producing large building blocks (namely, a shipyard which assembles prefabricated keel elements). The building blocks are very large, and, once a block is placed in the hall, it cannot be moved until all assembly operations on this block are complete. Each block must be processed during a predetermined time window. The objective is to maximize the number of building blocks produced in the hall.     

Dispersion and stability properties of radial basis collocation method for elastodynamics

Strong form collocation with radial basis approximation, called the radial basis collocation method (RBCM), is introduced for the numerical solution of elastodynamics. In this work, the proper weights for the boundary collocation equations to achieve the optimal convergence in elastodynamics are first derived. The von Neumann method is then introduced to investigate the dispersion characteristics of the semidiscrete RBCM equation. Very small dispersion error (< 1%) in RBCM can be achieved compared to linear and quadratic finite elements. The stability conditions of the RBCM spatial discretization in conjunction with the central difference temporal discretization are also derived. We show that the shape parameter of the radial basis functions not only has strong influence on the dispersion errors, it also has profound influence on temporal stability conditions in the case of lumped mass. Further, our stability analysis shows that, in general, a larger critical time step can be used in RBCM with central difference temporal discretization than that for finite elements with the same temporal discretization. Our analysis also suggests that although RBCM with lumped mass allows a much larger critical time step than that of RBCM with consistent mass, the later offers considerably better accuracy and should be considered in the transient analysis. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Convergence of a regularization method for creeping flow of a Bingham material about a rigid sphere

Creeping flow around a solid sphere is solved numerically using two regularized constitutive equations that approximate a Bingham material. The yield surface cannot be easily established from contours of the yield stress obtained with finite values of the regularization parameter due to numerical constraints. The outer yield surface can be estimated from the values of the normalized second invariant of the deformation rate that are invariant with respect to the regularization parameter, and the limiting solution for creeping flow of a Bingham material about a rigid sphere appears to be achieved.     

Speeds of sound,densities, isentropic compressibilities of the system (methanol + polyethylene glycol dimethyl ether 250) at temperatures from 293.15 to 333.15 K

In this work, our objective is to contribute to the knowledge of the mixtures (alcohol + polyalkyl ether glycol) used in absorption refrigeration systems and heat pumps. The determination of different thermophysical properties is essential to understand the interactions among different molecules in liquid mixtures. Therefore, experimental data of speed of sound and density together with calculated values of isentropic compressibility for the refrigerant-absorbent system (methanol + polyethylene glycol dimethyl ether 250) (or Pegdme 250) have been gathered here over the whole range of composition at temperatures from T=293.15 to 333.15 K and atmospheric pressure. The two previous experimental properties were measured with a digital vibrating tube analyser Anton Paar DSA-48. Also, the excess molar volumes and the increments of the speed of sound and the isentropic compressibility have been determined for each composition and they were fitted to a variable-degree polynomial equation.     

Mechanisms of stress transfer and interface integrity in carbon/epoxy composites under compression loading. Part II: Numerical approach

The finite element method is used to get an insight into the micromechanics of the compressive behaviour of carbon fibre composites. First the developed model is validated with existing experimental data and good agreement between predictions and experiments was found. Then the FE model is used to derive the complete stress field in the fibre and the matrix in the vicinity of a fibre fracture location. It was found that the perturbation of the stress field occurs mainly in the direction transverse to the fibre axis and this could explain the failure modes observed in composites tested in compression. Finally, a parametric study was performed on the effect of matrix modulus and matrix yield stress on the compressive fragmentation process.     

Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformation

Many composites consist of a fabric structure embedded in a matrix material. As an example, in the present paper, the case of pneumatic membranes is considered. Fibres are often made of material which shows noticeable plastic deformation. The stiffness of the fibres determines the overall stiffness of the material such that the correct modelling of the orthotropy of the composite is very important. In addition, the structure experiences large deformations which must be accounted for. Suitable models for this type of materials are therefore derived in the framework of finite anisotropic plasticity. A main problem is, however, the lack of experimental data in the literature. For this reason, a computer model of the composite is set up for numerical experiments. In this way, sufficient data can be generated. The present continuum mechanical model based on these “artificial” test data can be efficiently implemented into a finite element formulation. Using a special integration algorithm, the non-linear equation system consisting initially of 10 equations reduces to two non-linear scalar equations.