نشریه روش های عددی در مهندسی
سال سی و سوم شماره 1 (تابستان 1393)

Most solution methods for Partial Differential Equations (PDEs) find their unknowns through solving a linear system of equations. This step consumes a considerable part of total solution time, and hence accelerating the solution of linear systems of equations has been the subject of many researches. In this research we solve linear systems of equations on Graphics Processing Units (GPUs) using a tunable Sparse Matrix-Vector multiplication (SpMV) implemented in Open Computing Language (OpenCL). We use the Conjugate Gradient (CG) method to this end. Kernel parameters are set such that the linear system of equation is solved in the fastest way possible. For a better performance, two variants of CG which most comply the execution model in OpenCL are implemented and their performances are compared with ViennaCL library on CPU and GPU. In both variants, the kernels are fused to reduce the kernel launch overhead. The results show that the proposed method consistently outperforms the ViennaCL library on a wide range of test systems and problems.

Three dimensional turbulent flow in a stirred tank with moving blades has been numerically studied. For the numerical simulation, a 3D parallel flow solver has been developed based on the lattice Boltzmann method. The large eddy simulation method has been used for the turbulence modeling. To improve the accuracy of the flow simulation in stirred tanks, a commonly used boundary condition for moving walls as well as a proposed alternative boundary condition have been investigated in great details. The present investigations show that the proposed improved bounce back method generates accurate results compared with those obtained using commonly used force field method. However, the implementation of the proposed boundary condition is more difficult for cases with complex moving walls.

In this article, an exact finite strip method is developed for free vibration of axially moving thin sandwich plate made of functionally graded material (FGM). For this purpose, the plate is divided to several finite strips. Displacement function of the strip along direction perpendicular to moving direction is assumed sinusoidal. The function along another direction has an exponential form as satisfies the differential equation governing the vibration of such sandwich plates and the boundary conditions of the problem. By defining nodal displacement and nodal forces at any line of a finite strip, the exact stiffness matrix of the strip is extracted. This matrix is a transcendental function of natural frequencies, axial speed, membrane forces, volume fraction exponent, and other parameters of geometry and material characteristics of the problem. Using global stiffness matrix of the plate, the natural frequencies of the plate which is under in-plane forces and moves on several rollers are calculated. Comparison studies are performed to verify the validity of the present results. The exact vibration solutions obtained for such plates are indeed valuable as they serve as important benchmark solutions for checking the convergence and accuracy of numerical methods for the analysis of such plates.

Transverse vibration of a composite Euler-Bernoulli beam with any arbitrary concentrated masses is developed and analytically solved in this paper. First, dynamic governing equations of a cross-ply beam with taking into account of number, location and amount of concentrated masses as well as the effects of torsional behavior of composite layup (due to bending-twisting coupling) are derived. Concentrated masses are modeled by delta Dirac function. Then, the governing equations are solved for two different boundary conditions (simplysupported, clamped-free) to obtain frequency response and mode shapes. The results of the developed model are validated by the available analytical results in the literature. Thus, the effects of number, location and amount of concentrated masses on the torsional-bending vibration of a composite beam can be investigated.

An isogeometrical approach, based on using the superconvergent property of the Gauss integration points, for error estimation and stress recovery of two-dimensional problems was introduced by Hassani et. al. In this paper, the method is further developed to deal with the isogeometrical analysis of three-dimensional problems. To investigate the performance of the approach in using the optimal stress points, two 3D examples with available analytical solutions are taken into consideration. The obtained results are indicative of the good performance of the method in improvement of stress and error estimation of 3D problems in the isogeometric analysis method.

In this paper, a novel numerical limit analysis approach is presented for determination of lower bound of collapse load in the stability problems of soil mechanics by combining lower bound theory, Shepard's mesh-free technique and second order cone programming. Based on the proposed method, the domain of problem is simulated by nodes, and there is no need for traditional meshing process used in the conventional mesh-based numerical limit analysis approaches. To satisfy the conditions required for admissibility of stress field at the entire problem domain, a Voronoi cell is considered around each node and the stress gradient is smoothed in this Voronoi cell. As the Voronoi cells cover the entire domain, the obtained smoothed stress field leads to a rigorous lower bound solution. Based on the derived formulation, a computer code is developed and the accuracy and efficiency of proposed method is investigated at the end of the paper by solving some examples.

Present paper deals with the phenomenon known as self-sustained nuclear fission wave that is set up with establishment of the U-Pu cycle in a fast nuclear reactor. The safety arised from self sustained state of the wave and also 50%the possibility of initiation and evolution of the wave, the system comprised of neutron diffusion equation coupled with burn-up and kinetic equations have been considered. The linearizationmethod used to solve this systemnot only separates diffusion subsystem from reaction one but also simplifies greately dealing with several real hundred days of simulation. Space and time discretizations of the linearized diffusion subsystem were performed by 3D finite element and crank nicolson methods, respectively. The convergence of equation was carried out using the iterations based on the optimized BiCGStab(L) method. Rung-Kutta (5) method was used to solve the first order differential equations of the reaction subsystem since the concentrations of elements in the reaction subsystem changed slowly. Using the element by element FEMand BiCGSta (L) used for solving the systemdropped the required memory down to 1/10. Considering the long period of the simulation, 3D case of the problem and heavy computations, the OpenMp method was used to parallelize the code written in FORTRAN 95.

This paper aims at presenting a new two-stage algorithm to find or approaching global minimum for manipulator in optimization problems. It uses a combination of mathematical optimization method and an evolutionary approach. The mathematical method is based on the indirect solution of open loop optimal control problem and the evolutionary method is based on Genetic Algorithm (GA). Some initial guesses generated by GA to produce optimal solution by optimal control are used. Then, the cost function is calculated for every optimal solution and the best solutions are chosen for the next step. In the next step of the algorithm, these solutions are used to produce the new initial guesses. Optimal control problem is then solved for each guess again, and its cost is calculated. This process continues until the minimum cost value is achieved. In order to improve performance of the algorithm, a new GA operator is introduced in addition to the conventional GA ones to select the pair chromosomes for crossover. The proposed method eliminates the problem of optimal control which is trapped in local optimal point and tries to obtain the global minimum. The effectiveness of the method is shown by simulation.

Nowadays multilayer perceptrons (MLPs) are one of the most important and widely-used neural networks used as continuous measurable function with a desired accuracy. The second benefit is nonparametric data-driven nature of them which meansmultilayer perceptrons impose few prior assumptions on the underlying process. Being adaptive is the third advantage of MLPs. The adaptation of MLPs implies that in a nonstationary environment the accuracy and robustness of results are still countable. Utilizing fewer parameters is the fourth benefit of MLPs. Despite all these unique advantages of multilayer perceptrons, they suffer from some limitations such as negative relationship between number of inputs and the achieved performance, though using hybrid methods to overcome the limitations by means of a method alone and improving forecasting performance is achievable. Literature review suggests that by utilizing disparate and unrelated methods, we can obtain a new hybrid scheme capable of less variance or error. Hybridization of dissimilar methods can reduce the risk of using an inappropriate method. Usually, this is done based on this fact that the underlying process cannot easily be determined. The motivation behind using hybrid method is two folds: either single method cannot identify the true data generating process or cannot identify all the characteristics of the time series. In this paper, a new hybrid method of multilayer perceptrons is proposed which uses the self-organizational maps. The self-organizational maps are one of the most accurate tools in recognizing and analyzing the nonlinear multidimensional spaces. In the proposed method, inputs of the multilayer perceptron are firstly clustered by using a self-organizational map, and then variables in each cluster are combined together according to their effectiveness values. Empirical results of steel price forecasting in TehranMetal Exchange indicate that the efficiency of the proposed method is comparable to other methods.

In today's competitive world, customers want a faster response, higher reliability and greater flexibility in changing needs. These factors require manufacturers and service providers to find better ways to manage the flow of their organization, the progress and to maintain their survival. This paper investigated the problem of multi product multi-period in a two-level supply chain, including producers and distributors. Presented problem with the purpose of maximum profit of the whole chain and production quality has been modeled. As regards traditional optimization’s methods don’t provide possibility of considering more than one purpose easily in optimization, Instead, heuristic methods of usage tools of multi objective optimization provides easily with high quality also increase the speed of reaching to the optimization goal or near it. So a newmulti-objective optimization tool is presented based on differential evolution algorithm and optimal Pareto concepts for solving problems. The efficiency of this algorithm is demonstrated by comparing it’s numerical experiment results with those ofMODE algorithm and LINGO package. Computational results indicate that the proposed algorithm has better performance.