# A frequency domain boundary element formulation for dynamic interaction problems in poroviscoelastic media

2014-02-01
Argeso, Hakan
Mengi, Yalcin
A unified formulation is presented, based on the boundary element method, to perform the interaction analysis for the problems involving poroviscoelastic media. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices at a single step in terms of system matrices of boundary element method without solving any special problem, such as, unit displacement or load problem, as required by conventional methods. It further eliminates the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. The formulation is explained by considering a simple interaction problem involving an inclusion embedded in an infinite poroviscoelastic medium, which is under the influence of a dynamic excitation induced by seismic waves. In the formulation, an impedance relation is established for this interaction problem, suitable for performing the interaction analysis by substructure method, which permits carrying out the analysis for inclusion and its surrounding medium separately. The inclusion is first treated as poroviscoelastic, then viscoelastic and finally rigid, where the formulation in each of these cases is obtained consecutively as a special case of the previous one. It is remarkable to note that, a cavity problem where there is a hole in place of inclusion can be also considered within the framework of the present formulation. The formulation is assessed by applying it to some sample problems. The extension of the formulation to other types of interaction problems, such as, multi-inclusion problems, the analyses of foundations supported by a poroviscoelastic medium, etc., will be the subject of a separate study.
COMPUTATIONAL MECHANICS

# Suggestions

 A boundary element formulation for axi-symmetric problems in poro-elasticity Özyazıcıoğlu, Mehmet H; Özkan, M. Yener; Department of Civil Engineering (2006) A formulation is proposed for the boundary element analysis of poro-elastic media with axi-symmetric geometry. The boundary integral equation is reduced to a set of line integral equations in the generating plane for each of the Fourier coefficients, through complex Fourier series expansion of boundary quantities in circumferential direction. The method is implemented into a computer program, where the fundamental solutions are integrated by Gaussian Quadrature along the generator, while Fast Fourier Transf...
 A DRBEM Approach for the STOKES Eigenvalue Problem Tezer, Münevver; Türk, Önder (2016-07-04) In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes a promising tool to characterize such problems due to the fact that the boundary conditions on part or all...
 A unified approach for the formulation of interaction problems by the boundary element method Mengi, Y; Argeso, H (Wiley, 2006-04-30) A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid-solid and soil-structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods....
 A new time-domain boundary element formulation for generalized models of viscoelasticity Akay, Ahmet Arda; Gürses, Ercan; Göktepe, Serdar (2023-05-01) The contribution is concerned with the novel algorithmic formulation for generalized models of viscoelasticity under quasi-static conditions within the framework of the boundary element method (BEM). The proposed update algorithm is constructed for a generic rheological model of linear viscoelasticity that can either be straightforwardly simplified to recover the basic Kelvin and Maxwell models or readily furthered towards the generalized models of viscoelasticity through the serial or parallel extensions. ...
 A Novel Input Impedance Computation Method for Coaxial Probe Fed Microstrip Antennas by Utilizing Characteristic Modes Cetin, Metehan; Alatan, Lale (2017-07-14) A method to efficiently compute the input impedance of the coaxial probe fed microstrip antennas by using characteristic modes is proposed in this paper. The efficiency is achieved by defining a discontinuous source current at the feed location that models the current injected by the probe. The input impedance is simply expressed in terms of modal excitation coefficients and eigenvalues of each mode.
Citation Formats
H. Argeso and Y. Mengi, “A frequency domain boundary element formulation for dynamic interaction problems in poroviscoelastic media,” COMPUTATIONAL MECHANICS, pp. 215–237, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65923.