China
Africa
Explore chapters and articles related to this topic
Geotechnical challenges in very high speed railway tracks. The numerical modelling of critical speed issues
Published in António S. Cardoso, José L. Borges, Pedro A. Costa, António T. Gomes, José C. Marques, Castorina S. Vieira, Numerical Methods in Geotechnical Engineering IX, 2018
In this sense, several distinct numerical approaches can be followed, being the Finite Elements Method (FEM), the Finite Differences Method (FDM), the Method of Fundamental Solutions (MFS) and the Boundary Elements Method (BEM) among the most popular. Regarding solution methods, time domain analysis (explicit or implicit solution) or frequency domain analysis are the most common methods that can be applied. It should be stressed that frequency domain analysis is confined to the solution of linear problems since it is based in the overlapping of effects. On other hand, transportation infrastructures, such as roads or railways, can be faced as infinitive and invariant structures. In such cases, the 3D wave propagation solution can be obtained through the combination of distinct plane waves that propagate along the structure development direction. Therefore it is possible to apply a spatial Fourier transformation along that direction and to determine the 3D displacement field as a continuous integral of simpler bi-dimensional solutions, as () u3D=12π∫−∞+∞u2.5D(k1)eik1(x−x0)dk1
Geotechnical challenges in very high speed railway tracks. The numerical modelling of critical speed issues
Published in António S. Cardoso, José L. Borges, Pedro A. Costa, António T. Gomes, José C. Marques, Castorina S. Vieira, Numerical Methods in Geotechnical Engineering IX, 2018
In this sense, several distinct numerical approaches can be followed, being the Finite Elements Method (FEM), the Finite Differences Method (FDM), the Method of Fundamental Solutions (MFS) and the Boundary Elements Method (BEM) among the most popular. Regarding solution methods, time domain analysis (explicit or implicit solution) or frequency domain analysis are the most common methods that can be applied. It should be stressed that frequency domain analysis is confined to the solution of linear problems since it is based in the overlapping of effects. On other hand, transportation infrastructures, such as roads or railways, can be faced as infinitive and invariant structures. In such cases, the 3D wave propagation solution can be obtained through the combination of distinct plane waves that propagate along the structure development direction. Therefore it is possible to apply a spatial Fourier transformation along that direction and to determine the 3D displacement field as a continuous integral of simpler bi-dimensional solutions, as () u3D=12π∫−∞+∞u2.5D(k1)eik1(x−x0)dk1
The method of fundamental solutions for scattering of electromagnetic waves by a chiral object
Published in Applicable Analysis, 2023
E. S. Athanasiadou, I. Arkoudis
The method of fundamental solutions (MFS) is a numerical method for solving boundary valued problems when the fundamental solutions of the differential operators governing the problems are known. The main idea of the method is to approximate the solution by a finite linear combination of the fundamental solutions with the singularities distributed outside the domain of the solution and with unknown coefficients which have to be determined. The singularities can be either preassigned or can be specified together with the coefficients of the linear combination using the boundary conditions. The method was first proposed by Kupradze and Aleksidze [1] for some boundary valued problems for the Laplace equation and the elastostatics. In [2], Kupradze extended the method for corresponding problems for the Helmholtz equation as well as for the system of Maxwell's equations. A numerical version of this method was later proposed by Mathon and Johnson in papers [3,4]. In [5], Fairweather et al. studied the application of the MFS for scattering problems of acoustic and electromagnetic waves. Recent work concerning the MFS for mixed transmission problems for acoustic waves is done by Manelidze and Natroshvili [6] and for elastic waves by Buchukuri et al. [7]. Furthermore, in [8,9], Karageorghis and Lesnic studied the application of the MFS to inverse scattering problems.
The method of fundamental solutions for electroelastic analysis of two-dimensional piezoelectric materials
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2022
Juan Wang, Xiao Wang, Wenzhen Qu
The method of fundamental solutions (MFS) has been proved to be an efficient and highly accurate meshless boundary collocation method for solving many engineering applications.[28–32] In the MFS, the solutions are approximated by a set of fundamental solutions of the corresponding governing equations, which are expressed in terms of source points located outside the real computational domain. The unknown coefficients of the fundamental solutions can be determined so that the corresponding boundary conditions are satisfied in the least squares sense. The advantages and possible applications of the method can be found in Refs.[33–36] The objective of this paper is to document the first attempt to apply the MFS for the numerical solutions of 2D piezoelectricity problems. The accuracy and applicability of the method will be demonstrated on three benchmark numerical examples.