discrete singular convolution

Discrete singular convolution is a new numerical method that its ability to vibrational analysis has been demonstrated in the last decade. A lot of research on how to apply the complex boundary conditions of the different issues using this method is carried out and a variety of solutions have been proposed in this regard. Applying the boundary conditions in the governing equations of coupled shear walls, is a challenging issue. This paper proposes a new algorithm for applying the boundary conditions in the vibration analysis of coupled shear walls using the DSC method. In order to validate the proposed method, several samples were analyzed using this algorithm and the results were compared with the values obtained from three conventional numerical methods of Finite element (FEM), Differential quadrature (DQM) and Finite difference (FDM) methods. The great conformity was found between the results which emphasized the validity and integrity of the proposed method. In addition, the ability of the DSC algorithm was explored in terms of the computational speed, computational effort and the amount of computer memory required aspect and compared with the other conventional numerical approaches. It is concluded that the DSC is more efficient than the compared numerical methods from the results of this study.

Up-lift force is one of the efficient parameters in loading over different types of hydraulic structures. In order to determine up-lift force, seepage analysis is required. This force is usually computed in laminar seepage, where the Darci law is the governing equation. Methods of seepage analysis can be classified in three general categories: analytical, experimental and numerical. If Darci conditions are not appointed in media, the governing seepage equation in soil will be nonlinear and it does not any analytical solution, so numerical or experimental methods must be applied to solve the problem. This paper explores up-lift force through seepage analysis in non- Dacian flows. In general, researchers have issued two different categories for modeling of non Darcian flows. The first category considers the relationship between flow velocity and hydraulic gradient and the second one deal with equations between Darcy-Weisbach friction coefficient and Reynolds number. In this study, equations of first category between flow velocity and hydraulic gradient have been combined with flow continuity equation for non-Dacian seepage modeling through numerical methods. Recently, the discrete singular convolution (DSC) has been proposed and applied to many practical problems. The objective of this paper is to examine the DSC algorithm for solving the mentioned equations and to compare the DSC with finite volume (FV) method, whose advantage for seepage analysis has been documented. Comprehensive comparison study between DSC approach and well-known method of FV is obtained for estimating up-lift force over the foundation of a concrete dam. Results are compared with common Bligh method. Results of two numerical methods agree very well. Thus, DSC can be applied for nonlinear equations governing the seepage in porous media to calculate the up-lift force in non-Darcian seepage conditions. Furthermore, because of consideration of various parameters such as diameter of particles, different coefficients of non-Darcian seepage, it is observed that the DSC and FV approaches performs practically and computationally much better for this study rather than Bligh method. Moreover it is concluded that, although Bligh method was applied by designers without considering the flow regime, results indicate that DSC can be utilized for designing purposes when the sheet pile below the dam body is locating on downstream. However when the sheet pile below the dam body is located upstream, this method can not be used because the calculated up-lift force is not on the safe side.