International Journal of Computational Methods

This paper presents a numerical simulation method for the brittle rock failure process under compression, by combining the finite element method with micromechanics damage theory. When considering the rock as a homogeneous material, the initial elastic constant of each computational element is the same, but the microcrack distribution in the rock follows a statistical distribution. Consequently, in the loading process, microcrack propagation in each element is different, leading to an inhomogeneous distribution of changes in elastic constant. Under increased loading, this distribution will ultimately be reflected in the macro-failure mode of the rock. To investigate the macromechanics of the rock failure process, the damage variables and effective elastic constants are used to reflect the propagation of microcracks, thus coupling the micromechanics and macromechanics of the rock failure process. Finally, the paper demonstrates the numerical simulation method by simulating the failure of sandstone; these computational results show that the method performs well in simulating the mechanical characteristics of the brittle rock failure process.

Wildfire is one of the most significant disturbances responsible for reshaping the terrain and changing the ecosystem of a particular region. Its detrimental effects on environment as well as human lives and properties, and growing trend in terms of frequency and intensity of wildfires over the last decade have necessitated the development of efficient forest fire management techniques. During the last three decades, Forest Fire Decision Support Systems (FFDSS) have been developed to help in the decision-making processes during forest fires by providing necessary information on fire detection, their status and behavior, and other aspects of forest fires. However, most of these decision support systems lack the capability of developing intelligent fire suppression strategies based upon current status and predicted behavior of forest fire. This paper presents an approach for development of efficient fireline building strategies via intelligent resource allocation. A Genetic Algorithm based approach has been proposed in this paper for resource allocation and optimum fireline building that minimizes the total damage due to wildland fires. The approach is based on a simulation–optimization technique in which the Genetic Algorithm uses advanced forest fire propagation models based upon Huygens principles for evaluation of cost index of its solutions. Both homogeneous and heterogeneous environmental conditions have been considered. Uncertainties in weather conditions as well as imperfect knowledge about exact vegetation and topographical conditions make exact prediction of wildfires very difficult. The paper incorporates Monte-Carlo simulations to develop robust strategies in uncertain conditions. Extensive simulations demonstrate the effectiveness of the proposed approach in efficient resource allocation for fighting complex wildfires in uncertain and dynamic conditions.

Selecting the optimal service from a mass of functionally equivalent services with low time cost is significant. Previous research addressed this issue excessively relying on several kinds of optimization algorithms. In this work, we propose an approach that prunes redundant services and reduces search space of service selection on the basis of Skyline computing and context inference. We firstly adopt Skyline computing to prune redundant services. Then, we present the notion of context service based on context inference to further reduce the size of service selection problem. Finally, mixed integer programming is employed to find the optimal service from context services according to users' Quality of Service (QoS) requirements. Experimental results on a test bed indicate that our approach can find the optimal service with low time cost.

The boundary element method (BEM), along with the finite element and finite difference methods, is commonly used to carry out numerical simulations in a wide variety of subjects in science and engineering. The BEM, rooted in classical mathematics of integral equations, started becoming a useful computational tool around 50 years ago. Many researchers have worked on computational aspects of this method during this time.

This paper presents an overview of the BEM and related methods. It has three sections. The first, relatively short section, presents the governing equations for classical applications of the BEM in potential theory, linear elasticity and acoustics. The second describes specialized applications in bodies with thin features including micro-electro-mechanical systems (MEMS). The final section addresses current research. It has three subsections that present the boundary contour, boundary node and fast multipole methods (BCM, BNM and FMM), respectively. Several numerical examples are included in the second and third sections of this paper.

An effective algorithm for the finite-horizon linear quadratic continuous terminal control is proposed. It is the combination of existing continuous soft and hard terminal control. We apply the algorithm to the automatic landing control of OH-6A helicopters. Numerical demonstration shows that, whether noise exists or not, the algorithm has less computation time and less feedback gains than existing hard terminal control while generally achieving the same terminal accuracy. The optimization problem which represents the hard terminal control can be addressed by sweep method and transit matrix method. It is also discovered that transit matrix method is a crucial point for improving terminal accuracy.

The finite element method (FEM) has been successfully applied to solve continuum-based engineering problems, and the discontinuous deformation analysis (DDA) has emerged as a more attractive model than the continuum-based methods for rock engineering problems due to its intrinsic feature of block discontinuity at the contact boundaries. This paper presents a hybrid approach for two-dimensional problems which takes the advantage of both the FEM and the DDA in solving problems involving continuum and discontinuum domains. The hybrid FEM/DDA method, named as the nodal-based DDA (NDDA), significantly improves not only the accuracy of stress distribution inside the DDA block but also the computational efficiency. A cracking scheme based on failure time is introduced to the NDDA so that it can handle the crack propagation inside blocks. Two validating examples show that the newly developed NDDA can model the brittle fracture well.

A class of singularly perturbed boundary value problems (SPBVPs) for fourth-order ordinary differential equations (ODEs) is considered. The SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions. In order to solve them numerically, a method is suggested in which the given interval is divided into two inner regions (boundary layer regions) and one outer region. Two initial-value problems associated with inner regions and one boundary value problem corresponding to the outer region are derived from the given SPBVP. In each of the two inner regions, an initial value problem is solved by using fitted mesh finite difference (FMFD) scheme on Shishkin mesh and the boundary value problem corresponding to the outer region is solved by using classical finite difference (CFD) scheme on Shishkin mesh. A combination of the solution so obtained yields a numerical solution of the boundary value problem on the whole interval. First, in this method, we find the zeroth-order asymptotic expansion approximation of the solution of the weakly coupled system. Error estimates are derived. Examples are presented to illustrate the numerical method. This method is suitable for parallel computing.

The boundary elements method (BEM), manipulated genetic algorithm (MGA), conjugate gradient method (CGM), and cubic spline interpolation (CSI) are implemented to identify the shape of a cavity located inside a 2D solid body using displacements measured from a biaxial tension test. A fitness function which is defined as the squared differences between the computed and measured displacements is minimized. The BEM is used to solve the direct 2D elastostatics problem for the boundary displacements. The MGA is used as a robust explorer to find the best circular initial guess needed by the CGM to achieve convergence. The CSI is finally employed to draw the best curve through the points found by the CGM which depict the boundary of the cavity. Several example problems with different shapes of the cavity such as elliptic, pear, heart and egg shaped are solved. The effects of the size of cavity and measurement errors on the estimation process are investigated.

In this paper, an improved interpolating moving least-squares (IIMLS) method with nonsingular weight function is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The IIMLS method can overcome the difficulties caused by the singularity of the weight function in the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas. By combining the boundary integral equation (BIE) method with the IIMLS method, an improved interpolating boundary element-free (IIBEF) method is presented for two-dimensional potential problems. The IIBEF method is a direct meshless boundary integral equation method in which the basic unknown quantities are the real solutions to the nodal variables, and the boundary conditions can be applied directly and easily. Thus, it gives greater computational precision. Some numerical examples are presented to demonstrate the IIMLS and IIBEF methods.

Prediction and simulation of load-related reflective cracking in airfield pavements require 3D models in order to accurately capture the effects of gear loads on crack initiation and propagation. Furthermore, the size relations between aircraft landing gear, pavement area and reflective cracks make this a multi-scale problem. This paper presents a generalized finite element method (GFEM) based on the solution of interdependent global and local problems. The macro-scale component of the solution is approximated by a finite element global model, while the fine-scale is addressed by a local model. This allows accurate modeling of cracks in airfield pavements that are orders of magnitude larger than the critical zones in which the initiation of reflective cracking occurs. Two 3D pavement models are created for this study. The first model is subjected to the gear loading of a Boeing 777 aircraft. This example demonstrates the accuracy of solving a multi-scale pavement problem with a GFEM enriched with local problem solutions. The second problem studies the effect of the size of the local domain on the accuracy of the GFEM solution. The numerical simulations show that 3D multi-scale problems such as reflective cracks in airfield pavements, can be efficiently solved by a GFEM based on interdependent global and local problems.

In this paper, a numerical model is developed based on coupled boundary element–finite element methods (BEM–FEM) to minimize liquid sloshing pressure in trapezoidal tank with different sidewall angles. Different geometric shapes such as rectangular, cylindrical, elliptical, spherical and circular conical have already been studied for ship storage tanks by other researchers. In this paper, a new arrangement, i.e., trapezoidal containers is suggested for liquid storage tanks. The tank shape is optimized based on sloshing pressures and forces for a range of frequencies and amplitudes of sway motion and tank configuration. Fluid is considered to be incompressible and inviscid. Therefore, Laplace equation and nonlinear free surface boundary conditions are used to model the sloshing phenomenon. The results validated using available data showed that a new arrangement of trapezoidal storage panels has a better efficiency against sloshing phenomenon than the conventional rectangular tanks.

This paper deals with a-finite element method (FEM) based on a V-shaped notch corner tip stresses to solve generalized stress intensity factors (GSIFs) in 2D elastic bodies. The method does not need extremely refined meshes and special elements accounting for the analytical form of singularities around the V-shaped notch corner tip. The generalized stress intensity factors of the V-shaped notch problems are evaluated from the ratios of FEM stress values at the notch corner tip for a given problem and a reference one. Several numerical examples show that present method is effective and applicable to dealing with the V-shaped notch problems.