Parallel computation of 3-D soil-structure interaction in time domain with a coupled FEM/SBFEM approach

The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-011-9551-xThis paper introduces a parallel algorithm for the scaled boundary finite element method (SBFEM). The application code is designed to run on clusters of computers, and it enables the analysis of large-scale soil-structure-interaction problems, where an unbounded domain has to fulfill the radiation condition for wave propagation to infinity. The main focus of the paper is on the mathematical description and numerical implementation of the SBFEM. In particular, we describe in detail the algorithm to compute the acceleration unit impulse response matrices used in the SBFEM as well as the solvers for the Riccati and Lyapunov equations. Finally, two test cases validate the new code, illustrating the numerical accuracy of the results and the parallel performances. © Springer Science+Business Media, LLC 2011.Jose E. Roman and Enrique S. 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An Efficient Coupled FEM-SBFEM Approach to Analyse Soil-Structure-Interaction in Time Domain

Bauwerke sind auf den umgebenden Baugrund gegründet, sodass Baugrund und Bauwerk miteinander interagieren können. Dabei können in den Baugrund eingeleitete Erschütterungen in die angrenzenden Gebäude übertragen werden. Zusätzlich interagieren benachbarte Bauwerke, wenn diese über den Baugrund miteinander verbunden sind. Heute ist die erdbebensichere Auslegung von Strukturen in seismisch aktiven Regionen oder auch die Komfortsteigerung von Gebäuden, indem diese von umgebenen Emissionen wie z.B. eingebrachten Vibrationen durch Verkehr oder Maschinenfundamente entkoppelt werden, von großem Interesse. Bei der Bearbeitung dieser sehr unterschiedlichen Fragestellungen wird immer häufiger auf numerische Simulationen zurückgegriffen, um die Boden-Bauwerk-Interaktion (BBI) zu untersuchen. In dieser Arbeit wird gezeigt, dass die Simulation der BBI unter Berücksichtigung randloser Gebiete, die die Sommerfeld'sche Abstrahlbedingung exakt erfüllen auch für großskalige realitätsnahe Modelle, wie sie in der Praxis benötigt werden, möglich ist. Dafür wird mit zwei numerischen Methoden ein effizientes gekoppeltes Verfahren zur Simulation der BBI im Zeitbereich vorgeschlagen. Die numerische Umsetzung beruht auf einer Kombination von FEM und SBFEM. Die FEM bildet dabei das Nahfeld ab, in dem die zu untersuchende Struktur samt anstehenden Baugrund enthalten ist. Der angekoppelte unendliche Halbraum wird als Fernfeld mit der SBFEM diskretisiert. Weil die Simulation der BBI im Zeitbereich mit einem großen Rechenaufwand und Speicherbedarf einhergeht, werden unterschiedliche Methoden eingesetzt um eine numerische Simulation in angemessener Zeit durchführen zu können. Es wird gezeigt, dass bei entsprechender Diskretisierung des Fernfeldes realitätsnahe Fragestellungen der BBI untersucht werden können. Verschiedene Ansätze werden für die Reduktion des Berechnungsaufwands verfolgt und miteinander kombiniert. Nach Einführung in die theoretischen Grundlagen der Modellbildung und einer Diskussion der numerischen Verfahren wird auf die Validierung des hier gewählten Kopplungsansatzes eingegangen. Dies erfolgt anhand ausgewählter Beispiele, für die analytische bzw. semi-analytische Lösungen bekannt sind. Es werden mögliche Anwendungen aus dem Bereich der Geotechnik vorgestellt und die Anwendbarkeit des hier entwickelten Verfahrens an Modellbeispielen gezeigt.Buildings are directly in contact with surrounding, such that the soil and the structure interact with one other. Consequently, soil induced vibrations are transmitted to the structures. Additionally nearby structures interact with one another as they are connected by the soil. Nowadays numerical simulation of soil-structure-interaction (SSI) is of great interest, and is applied to a wide range of different problems. These include the analysis and design of reliable earthquake-resistant structures in seismic active areas, and also design to the increase the comfort of buildings by decoupling them from surrounding emissions such as vibrations induced by traffic of machine foundations. The present work shows the simulation of SSI which takes unbounded domains into account. This work fulfils the Sommerfeld radiation condition exactly, and shows that it is not only applicable for academic examples, but for large scale real life problems as well. Two numerical methods are coupled to create an efficient coupled method which can be used to simulate soil-structure-interaction in the time domain. The numerical implementation of this coupled approach is based on a combination of the FEM and the SBFEM. The FEM is used to discretise the near field, containing structures and its surrounding soil. The coupled infinite half-space the so called far field is realised by the SBFEM. The simulation of SSI in the time domain is computationally very time and memory intensive. Different methods are used to perform numerical simulations in the appropriate time. It is shown that using a suitable optimisation of the far field, realistic problem analysis of the SSI can be realised, therefore various optimisation approaches are used and combined with each other. Additionally a contemporary parallel implementation of the algorithms is done. After introducing the theoretical background and discussing the chosen numerical approach, a validation of the used coupling scheme is done. This validation is carried out by comparison of numerical and analytic solutions for defined test cases. Subsequently the numerical performance of the implemented software is tested in terms of speed-up and efficiency. Finally, different geotechnical applications are illustrated and the applicability of the coupled method is shown and discussed using examples