نشریه روش های عددی در مهندسی
سال سی و سوم شماره 2 (زمستان 1393)

In this paper, the numerical integration needed in the element free Galerkin method is improved, using Kriging interpolation. In the presented method, integrand is replaced by a surface which is produced by simple Kriging. Then the weights of integration points are calculated. Since the surface produced by simple Kriging is obtained by cloud of points and without back ground mesh, the weights of integration points are calculated in one step in the whole domain and without any element. Although any mesh free interpolation approach can be used in this procedure, simple Kriging is easier and more applicable. On the other hand, Kriging method is used for construction of shape functions. Hence, due to the satisfaction of Kroneker delta, essential BC can be easily implemented. The present method is used in 2-D elasto-static problems and effectiveness is proven.

In the present study, by employing the statistical properties of random variables at design point and mode a new method is presented to rank random variables in original space. This method obviates the need for derivation from limit state function and just needs to know the coordinate of design point. Also, in order to determine design point in the original space, an algorithm based on a weighted method and particle swarm optimization method is presented providing the possibility ofdetermining design point accurately without mapping. Robustness and accuracy of the proposed methods is evaluated by solving some numerical and engineering problems. The obtained results compared with exact solutions confirm the efficiency of the proposed methods for solving various engineering problems.

When high concentration of sediment is carried by the river, a settling basin design is required at the intake. In the present research, a three-dimensional numerical model was developed to simulate settling basin sedimentation. For the simulation, time averaged Navier-Stokes equations (RANS) as flow governing equations, convection-diffusion equation for suspended sediment concentration, and Van-Rijn bed load equation for boundary condition in the bed were used. Numerical solutions of the flow governing equations were suggested to be finite volume spatially and finite difference temporally. Decoupling procedure of the pressure was derived from MAC. Finite volume method was applied to discretise the convectiondiffusion equation for the suspended sediment equation. The predicted results proved comparable with the observed experimental data. Thereafter, the model was successfully applied to a real case study in Nekoabad settling basin.

In the present work, mixing of two species induced by a rotating cylinder confined in a channel is investigated using overset grid method and the effect of variation of Reynolds number, rotational velocity of the cylinder and blockage ratio on the structure of flow and wakes and mixing mechanism is studied. Numerical simulations are performed at Reynolds numbers of 10, 70 and 100, non dimensional rotational rates of 0, 1 and 2, blockage ratios of 0.1, 0.3 and 0.5 and Schmidt numbers of 1 and 4. In unsteady flow past a circular cylinder confined in a channel, the pattern of shed vortices is different from that observed in free stream flow past a cylinder and the vortices behind the cylinder moves criss-cross. The vortex shedding from the cylinder enhances mixing of species in channel. The vortex shedding behind the cylinder is weakened by rotation of the cylinder. The results show that as blockage ratio increases, mixing index near the exit of the channel decreases.

Proton exchange membrane (PEM) fuel cell performance is directly related to the bipolar plates design and their flow field. The bipolar plate design plays a significant role in the reactant and current density distributions, and water and heat, management in a PEM fuel cell, thereby improving the cell performance. In this study, a novel configuration of flow field in the bipolar plate, a honeycomb flow field, is proposed, where the flow-field network is formed by many hexagonal pins arranged in a regular pattern. A set of governing equations, conservation of mass, momentum, species, energy and charge, as well as electrochemical kinetic for all regions of fuel cell are considered and developed numerically while the model is treated as a singledomain by presenting a three-dimensional model. Through this model, the effects of honeycomb flow field on the oxygen transport, oxygen and current density distributions, water transport, pressure drop across the channel and PEM fuel cell performance are investigated. The main design criteria in this research are based on more oxygen and current density distribution uniformity, higher voltage, power density output, and low pressure drop. The results reveal that in the PEM fuel cell with honeycomb flow field, an enhancement in the oxygen transport, uniform oxygen and current density distribution, higher voltage and power density output at the catalyst surface, especially at the positions right beneath the locations of pins occurrs although the pressure drop across the channel increases.

The effect of Reynolds number and inclination angle on the behavior of drops suspended on an inclined surface at high viscosity ratio is studied by numerical simulations at non-zero Reynolds number. The flow is driven by the acceleration from gravity without any pressure gradient in the flow direction. It is found that by increasing Reynolds number, drops close to the floor or close to the free surface move to the center of channel and the equilibrium position moves away from the channel floor, increasing the fluctuation energy as well. The same trend is observed when the inclination angle with respect to horizontal direction increases. That is, when the inclination angle of the channel with respect to horizontal direction increases, drops close to the floor or close to the free surface move to center of the channel. The equilibrium position moves away from the channelfloor and fluctuation energy increases.

The approach of continuum mechanics is employed for modeling single layer nanoplates in order to study their buckling behavior. In this regard, different constitutive equations including differential non-local, second order strain gradient, implicit gradient, and modified couple stress theories are employed to develop the buckling governing equations of Graphene Sheets. In the numerical study, the effects of a few variables including size effect parameter, nanoplate size, and boundary conditions on the buckling behavior are investigated.

In this study, a computational study was carried out on the interaction between matrix cracking and delamination. The study also investigated in homogeneous simulation of fiber and matrix of 90o ply in front of delamination and their effects on the fracture properties of the double cantilever beam (DCB) test specimens prepared by cross ply laminates. It seems that the most important cause of the difference between mode-I critical strain energy release rate (GIc) of multidirectional (MD) laminates and that of unidirectional (UD) laminates is due to the difference in damage mechanisms. One of the most important kinds of damage mechanisms in MD laminates is matrix cracking. For simulation and prediction of matrix cracking and delamination, preexisting cohesive elements were used. The results indicated that simultaneous simulation of matrix cracking and delamination can predict a 15-percent increase in the GIc of MD laminates. Another cause of the difference in GIc might be nonuniform stress field resulting form fiber and matrix in delaminated front. In homogeneous simulation of 90o ply can cause a 26-percent increase in the GIc of MD rather than UD laminates.

Estimation of hydrodynamic forces is the first step in the design of submersibles. The hydrodynamic forces are expressed in terms of hydrodynamic coefficients. In this paper, to calculate the damping coefficients a method based on calculation of variation of the Drag and Lift coefficients with angles of attack and drift is described. The method is used to calculate the damping hydrodynamics of the Suboff submarine. A new method is also described in order to calculate the linear added mass coefficients of the submarine in axial and lateral directions. The method is validated by comparing its results with the known results for the added mass coefficient of a sphere. The numerical results agree well with the available experimental results of the submarine.

In this paper, the effect of stacking sequence on strain energy release rate (SERR) distribution is numerically investigated in the laminated end notch flexure (ENF) specimens. ENF specimens are three-dimensionally modeled in finite element software ABAQUS, and strain energy release rate is calculated by virtual crack closure technique (VCCT). Numericalresults for different lay-ups showed that the available non-uniformity ratio in the literature only depends on bending moduli and does not consider the effects of other moduli. Therefore, a new parameter which is dependent on both flexural and extensional moduli is proposed for symmetric ENF specimens. Finally, a method for estimation of critical SERR in multidirectional ENF specimens is introduced based on the equivalent layup approach. In fact, each multidirectional laminate is simplified by an equivalent unidirectional laminate so that both layups have the same flexural rigidities.