Soil Dynamics and Earthquake Engineering (02677261)175
One of the main problems of nonlinear time history analysis is its high computational effort, especially in structures with large number of structural components, high-rise buildings and complex structural systems. The ground motions recorded in recent years also include more recorded points than in the past, which has also increased the required volume of calculations. In this paper, three downsampling methods for reducing calculation costs of nonlinear time history analysis are presented and their applicability is investigated through practical examples of complex structures. These methods include the discrete wavelet transform, the time step correction, and the wavelet time step correction which is introduced in this paper. The efficiency of these downsampling methods is investigated for near-fault and far-fault earthquake records, as well as for records on different soil types. A comprehensive study is performed on five sets of ground motions consisting of 20 records. Each record is filtered up to three stages using one half, one quarter, and one eighth of the number of the main record points. First the linear and nonlinear response spectra based on the original records and the approximate waves are investigated. Subsequently, to evaluate the performance of the methods on more complex structural systems, two three-dimensional structures of 6-story and 15-story are analyzed. The 6-story structure is equipped with viscous dampers, while the 15-story structure has seismic isolators. The results indicate that the wavelet time step correction method has better performance in most cases, compared to the other two methods. It is shown that careful consideration is needed when dealing with earthquake records with high frequency contents. In such situations, one filtering step for the discrete wavelet transform method and two filtering steps for the other two methods are recommended. Also, in practical applications, it is advisable to choose earthquake records exhibiting the least error based on the results of SDOF systems analyses. Employing this technique can significantly cut down computational effort (up to 90%), while maintaining an average error ranging from 1% to 2% for the wavelet time step correction method. © 2023
Ocean Engineering (00298018)134pp. 176-177
In this reply, we re-emphasize on the fact that in the simulation of inviscid incompressible fluid flows using Lagrangian description, under some conditions, the divergence operator and the material derivative operator commute and thus the Laplace of the pressure is applicable in practical engineering problems as it has already been used and verified in numerous studies by many researchers. We show that the incompressibility condition suggested by the author of the discussion (discusser), as the replacement for divergence of the velocity field in using finite time increments, is insufficient and wrong. It will be shown that the concept has totally been misinterpreted by the discusser. © 2017 Elsevier Ltd
Ocean Engineering (00298018)122pp. 54-67
In this paper, it is first proven that instead of Poisson's equation one can use Laplace's equation for the pressure, which is much simpler to solve, in Lagrangian simulation of incompressible inviscid Newtonian fluid flow problems starting from a divergence-free initial acceleration condition. When Laplace's equation for the pressure is used in Newmark time integration scheme it guarantees mass conservation with O(Δt3) accuracy. Next in this paper a consistent 3D mesh-free method for the solution of free surface sloshing in tanks is presented. In this method a linear summation of exponential basis functions (EBFs) is assumed as an approximation to the solution. The coefficients of the series are determined by a collocation technique used on a set of boundary nodes. These coefficients and the surface boundary nodes are updated through a time marching algorithm. Linear/non-linear 3D sloshing problems are solved in both rectangular and cylindrical basins. It is shown that the method may be used as an effective tool for 3D simulation of tanks with various shapes without the need for a huge number of domain/boundary elements for the discretization. © 2016 Elsevier Ltd
Journal of Computational Physics (10902716)231(2)pp. 505-527
In this paper, a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries. A Lagrangian formulation established on pressure, as a potential equation, is employed. In this method, the approximate solution is expressed by a linear combination of exponential basis functions (EBFs), with complex-valued exponents, satisfying the governing equation. Constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique. The numerical solution is performed in a time marching approach using an implicit algorithm. In each time step, the governing equation is solved at the beginning and the end of the step, with the aid of an intermediate geometry. The use of EBFs helps to find boundary velocities with high accuracy leading to a precise geometry updating. The developed Lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems. Non-linear sloshing fluids in rigid rectangular two-dimensional basins are particularly addressed. © 2011 Elsevier Inc.
Journal of Computational Physics (10902716)231(21)pp. 7255-7273
In this paper exponential basis functions (EBFs) satisfying the governing equations of elastic problems with incompressible materials are introduced. Due to similarity between elasticity problems and steady state fluid problems the bases found for the former problems are used for latter problems. We discuss on using single field form known as displacement/velocity based formulation and also on using a two-field form known as u-p formulation. In the first formulation we find the pressure bases through performing a limit analysis using a fictitious bulk modulus while in the second formulation the bases are found directly by considering the pressure as a separate variable. In the second formulation we directly apply the condition of incompressibility. It is shown that both formulations yield identical bases meaning that the first one may be used in a standard approach. However, it is also shown that when the incompressibility condition is applied by a Laplacian of pressure in the second formulation, some additional spurious EBFs may be obtained. Having defined appropriate bases, we follow the solution strategy recently introduced by the authors for other engineering problems. Some well-known benchmark problems are solved to show the capabilities of the method. © 2012 Elsevier Inc.
In this paper, exponential basis functions (EBFs) are used in a boundary collocation style to solve elasticity and steady Navier-Stokes equations in problems with fully incompressible materials. In the presented method, the approximate solution of the standard form of elasticity and Navier-Stokes equations is expressed by a linear combination of EBFs with complex-valued exponents multiplied by polynomials. Constant coefficients of the solution series are evaluated through a point collocation method on the domain boundaries via a complex discrete transformation technique. With these basis functions, the standard equations can be solved with Poisson's ratio equals to 0.5. Furthermore, Pressure basis functions can be straightforwardly evaluated by calculating the limit of bulk modulus multiplied by volumetric strain when Poisson's ratio approaches to 0.5. Some benchmark problems have been solved to show the capabilities of the method. © 2010 Civil-Comp Press.
