International Journal of Computational Engineering Science

This paper introduces an object-oriented programming approach into the development of a general-purpose simulation framework for the numerical modeling of microstructure evolution at the mesoscopic length level. The design requirements of this framework are discussed, and an analysis from the standpoint of object-oriented programming is performed. Based on this framework, a Monte Carlo grain growth algorithm with improved efficiency and accuracy has been developed. This simulation framework is expected to represent a reliable software module of a multi-scale microstructure prediction system for materials processing.

The problem concerning with a nonlinear laminar boundary layer, heat and mass transfer flow of an incompressible, viscous and electrically conducting fluid past a continuously moving infinite vertical porous plate under the influence of a uniform magnetic field is considered. Consideration is given to heat source and thermal diffusion. A similarity transformation has been utilized to convert the nonlinear partial differential equations into nonlinear ordinary differential equations. The numerical solution of the problem is obtained using the Runge Kutta Gill method. Velocity, temperature and concentration fields are shown graphically to study the effects of parameters entering into the problem. Analysis of the results shows that the flow field is influenced appreciably by the presence of suction at the surface, chemical reaction and magnetic effects.

Realistic mechanical wave propagation problems and acoustic problems in transient dynamics with a broad frequency range require very large systems and many timesteps, to obtain reliable numerical solutions with sufficient high accuracy. New algorithms are to be developed to make effective use of todays hardware features and the visualization of complex prozesses like intensity and energy flow in transient dynamics.

The propagation of mechanical waves is characterized by the change and interaction of strain energy and kinetic energy in space and time. A fast explicit FD-algorithm for wave propagation problems and acoustic problems is developed to analyse and visualise the complex behavior of traveling waves. This inherent parallel algorithm is based on the solution of the three-dimensional wave equation as a first order formulation in terms of stresses and velocities or acoustic pressure and particle velocity, representing both forms of energy in a direct way. Because of the small storage required and the short computational time, the algorithm allows numerical investigations of large systems with online graphic simulations to analyse the complex real physical behavior of propagating waves and to make numerical results comparable to measured results. Local mesh refinement helps to minimize numerical errors of the discrete model.

Examples of applications are given with dispersional effects of traveling waves, instantaneous intensity distribution and local energy flow of propagating and standing waves. The complex behavior of traveling waves in a bar with a crack is analysed as a three-dimensional system. As a result, a non-destructive testing method is described using impact hammer for the detection, localization and quantification of cracks. The size of the defects can be of some order smaller than the used wave length.

We review critically the performance of an ingeniously designed hybrid beam element that uses a stiffness matrix based on Timoshenko theory but retains the mass matrix from classical beam theory. This clever engineering trick gives seemingly very accurate results in thin beam situations. However, the physics of thick beam behavior is consequently misrepresented. A careful study reveals that cancellation of errors is responsible for the apparent "accurate" performance.

Most of the work in the field of topology optimization is concentrated on using sensitivity analysis and optimality criteria methods that need explicit formulation. The design systems are often hard-coded for a specific problem with specialized optimization and FEM routines. This paper presents a work that uses a system approach to solid free form design. It attempts to develop a general topology optimization system that has a wide range of applicability by making use of sophisticated optimization and FEM packages available. A computer design system is implemented with an integration of commercial codes CFSQP and NASTRAN. A pre-processor and a post-processor are developed to assist the optimal design process. The system is tested with benchmark cases for minimum mean compliance and minimum weight designs. The results for the cases are presented, demonstrating the ability of the system to handle complex cases with practical feasibility. The implementation is evaluated with a parametric study of its performance. The key factors for the common problems of topology optimization are examined, including the mesh dependency and numerical instability. The computational efficiency is further studied to indicate the direction for further improvement of the system.

Most existing curved beam elements suffer from poor convergence difficulties and a heavy computational burden while limit themselves to 2D problems. In this paper, we address and overcome these difficulties by developing a new three-noded locking-free 3D curved beam element. The element formulations, which employ coupled consistent polynomial displacement fields, satisfy the membrane locking-free requirement of being able to recover the inextensible bending mode of the curved beam. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results of two- and three-dimensional applications are presented to demonstrate the superior accuracy and high convergence rate of the newly developed curved beam element compared with existing ones.

The classical approach to linking lattice dynamics properties to continuum equations of motion, the "method of long waves," is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the first part of the article, the derivation is made within the harmonic approximation for the perfect lattice response. Higher order terms are included in the continuum equation of motion to account for non-linear dispersion effects. Wave propagation coefficients as well as fourth order dispersion coefficients are obtained. In the second part, the lattice anharmonicity is considered and nonlinear macroscopic equations of motion are obtained within the local approximation. Both continuum solutions are particularized to the one-dimensional case and are compared with the lattice response in order to establish the accuracy of the approximation.

The paper presents and discusses the parallelized 3D finite-difference time-domain algorithm based on single-program multiple-data architecture using the MPI protocol for electromagnetic compatibility and signal integrity analysis and evaluation in high-speed designs. The efficiency for parallelization is verified through numerical experiments at IBM P640 and P690 multiprocessor high performance computers with up to 20 processors at different sizes of the problems.

In the present paper a simple mixed-hybrid element for the linear analysis of Reissner-Mindlin plates is discussed. The element is derived from a modified Reissner functional and standard bilinear (isoparametric) interpolation for displacement and rotations is assumed whereas local stresses (rather than stress resultants and moments) are explicitly modelled. It is assumed that in plane shear stresses are not a priori symmetric. This choice allows to decouple the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling degrees of freedom. Out-of-plane shear stresses are then obtained such that equilibrium equations are exactly satisfied. The proposed element does not exhibit locking effects at all: i.e. the shear deformation energy is zero in the thin plate limit. Details of the formulation are provided, and the performances of the element are assessed with reference to well-established benchmark problems.

In this paper we present an efficient numerical one-step method of high order in space and time for solving the elastic-plastic wave equation in three space dimensions. The basic idea is to decompose the hyperbolic PDE into advection equations, which can be solved numerically, Furthermore, the occurrence of plasticity makes it necessary to solve an ODE for the stress-strain relationship at every point.

Genetic algorithms have been applied to many optimization and search problems and shown to be very efficient. However, the efficiency of genetic algorithms is not guaranteed in those applications where the search space is small, such as the block motion estimation in video coding applications, or equivalently the chromosome length is relatively short, less than 5 for example. Since the characteristics of these small search space applications are far away from the conventional search problems in which the common genetic algorithms worked well. New treatments of genetic algorithms for dealing with the small range search problems are therefore of interest. In this paper, the efficiency (will be defined later) of the genetic operations of common genetic algorithms, such as crossover and mutation, are analyzed for this special situation. As expected, the so-obtained efficiency/performance of the genetic operations is quite different from that of their traditional counterparts. To fill this gap, a lightweight genetic search algorithm is presented to provide an efficient way for generating near optimal solutions for these kinds of applications. The control overheads of the lightweight genetic search algorithm is very low as compared with that of the conventional genetic algorithms. It is shown by simulations that a lot of computations can be saved by applying the newly proposed algorithm while the search results are still well approved.

This paper presents two robust algorithms for calculating the orientation and inclusion of simple polygons, respectively. By finding a maximum vertex of a simple polygon, a very fast convex vertex searching method is proposed and the orientation of the polygon can be uniquely determined. To decide the relationship between a point and a simple polygon, the concept of visible edge is put forward and an efficient visible edge searching algorithm is presented.

The salt-gradient solar ponds are considered in this work in order to study its performance numerically. Governing equations of the upper convective zone, nonconvective zone, and lower convective zone of a salt gradient solar pond are deduced as a set of non-linear partial differential equations. The equations are solved numerically to predict the thermal performance of the solar pond over a long time. The meteorological data of Egypt such as incident solar radiation, ambient temperature, air velocity, and relative humidity are taken into considerations in the model. Heat transfer modes considered between the upper convective zone and the ambient are convection, evaporation, and radiation. The present model is used to study the development of temperature inside the three zones of salt gradient solar pond. The optimum thickness of each layer is obtained with close agreement of previous results.

The propagation of fronts in two–dimensional, anisotropic, nonlinear reactive–diffusive media with cross–diffusion is analyzed by means of implicit time–linearized factorization techniques. Four factorization methods are considered; the first one disregards the approximate factorization errors and treats the mixed second–order derivatives explicitly, whereas the other three account for either the approximate factorization errors or the mixed second–order derivative terms in an iterative manner. The four techniques involve the solution of one–dimensional operators and require the solution of linear algebraic systems with block–tridiagonal matrices. It is shown that anisotropy and cross–diffusion deform the reaction front and affect the front velocity. It is also shown that the approximate factorization method that treats the mixed second–order derivative terms iteratively provide much more accurate transient results than techniques that account for the approximate factorization errors and treat the mixed second–order derivative terms in an explicit manner.

We propose a multi-dimensional scheme to solve the shallow water equations by using the CIP(Constrained Interpolation Profile/Cubic Interpolated Pseudoparticle) method which has the accuracy by one-order of magnitude better than the cubic Lagrange. This third-order accuracy is kept even in non-uniform grid, while the cubic Lagrange becomes the first order. The semi-Lagrangian approach to the characteristic equations has been used for solving gravity waves because it can make time step be much longer than the Courant-Friedrichs-Lewy (CFL) condition. Even in two dimensions, the method can give a symmetrical wave propagation under the large CFL condition.