Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

Hermanns, Lutz Karl Heinz and Rey Llorente, Ignacio del and Fraile de Lerma, Alberto and Alarcón Álvarez, Enrique (2005). Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method. In: "10th. International Conference on Civil, Structural and Environmental Engineering Computing", 30/08/2005-02/09/2005, Roma (Italia). ISBN 1-905088-02-7.

Description

Title: Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method
Author/s:
  • Hermanns, Lutz Karl Heinz
  • Rey Llorente, Ignacio del
  • Fraile de Lerma, Alberto
  • Alarcón Álvarez, Enrique
Item Type: Presentation at Congress or Conference (Article)
Event Title: 10th. International Conference on Civil, Structural and Environmental Engineering Computing
Event Dates: 30/08/2005-02/09/2005
Event Location: Roma (Italia)
Title of Book: Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing
Date: 2005
ISBN: 1-905088-02-7
Subjects:
Freetext Keywords: Similar Coefficient Identification Algorithm (SCIA); Boundary Element Method (BEM); wave propagation ; Soil-Structure Interaction (SSI); pile foundations ; dynamic stiffness
Faculty: E.T.S.I. Industriales (UPM)
Department: Mecánica Estructural y Construcciones Industriales [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

More information

Item ID: 20053
DC Identifier: http://oa.upm.es/20053/
OAI Identifier: oai:oa.upm.es:20053
Official URL: http://www.ctresources.info/ccp/paper.html?id=269
Deposited by: Biblioteca ETSI Industriales
Deposited on: 17 Sep 2013 10:57
Last Modified: 21 Apr 2016 22:20
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