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. Quintana-Orti were partially supported by the Spanish Ministerio de Ciencia e Innovacion under grants TIN2009-07519, and TIN2008-06570-C04-01, respectively.Schauer, M.; Román Moltó, JE.; Quintana Orti, ES.; Langer, S. (2012). Parallel computation of 3-D soil-structure interaction in time domain with a coupled FEM/SBFEM approach. Journal of Scientific Computing. 52(2):446-467. doi:10.1007/s10915-011-9551-xS446467522Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Croz, J.D., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK User’s Guide. Society for Industrial and Applied Mathematics, Philadelphia (1992)Antes, H., Spyrakos, C.: Soil-structure interaction. In: Beskos, D., Anagnotopoulos, S. (eds.) Computer Analysis and Design of Earthquake Resistant Structures, p. 271. Computational Mechanics Publications, Southampton (1997)Appelö, D., Colonius, T.: A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems. J. Comput. 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Implementation of an efficient coupled fem-sbfem approach for soil-structure-interaction analysis

Buildings are grounded in the surrounding soil, so that soil and structure interact with each other. Consequently in the soil induced vibrations are transmitted to the structures. Neighbouring buildings and structures interact with each other, as they are connected by the soil. Nowadays numerical simulation of soil structure interaction is of great interest and is applied to very different problems. These include for example the construction of reliable earthquake-resistant structures in seismic active areas, and also the increase of comfort of buildings by decouple them form surrounding emissions like vibrations induced by traffic of machine foundations. This work shows that the simulation of soil-structure-interaction taking unbounded domains into account, which fulfils the Sommerfeld radiation condition exactly, is not only possible for academic examples, but for large scale real life problems as well. Therefore two numerical methods where coupled to create an efficient coupled method, which can be used to simulate soil-structure-interaction in time domain. The numerical implementation of this coupled approach bases on a combination of finite element method [1] and scaled boundary finite element method [2]. The finite element method is used to discretise the near-field, containing structures and its surrounding soil. The coupled infinite half-space, the far-field is realised by the scaled boundary finite element method. A contemporary parallel implementation of the coupling algorithms is done, since the simulation of soil structure interaction in time domain is very time and memory consuming [3]. Subsequent the numerical performance of the implemented software is discussed in terms of speed-up and efficiency. Different geotechnical applications are illustrated and the applicability of the coupled method is shown and discussed on chosen examples

Parallel application on high performance computing platforms of 3D BEM/FEM based coupling model for dynamic analysis of SSI problems

Implementation of an improved parallel computation algorithm into a coupled model based on Finite Element and Boundary Element Methods for analysis of threedimensional Soil-Structure Interaction (SSI) problems on High-Performance Computing (HPC) platforms is presented. The model and the parallel computation algorithm are developed for the linear analysis of large-scale three-dimensional SSI problems. The finite element method is used for modeling the finite region and the structure, and the Boundary Element Method is used for modeling the soil extending to infinity. The parallelization of the model is performed by the calculation of the impedance coefficients on the interaction nodes between the near- and the far-fields. The performance of the parallel computation algorithm is represented by elapsed timing measurements according to the number of processors. The efficiency of the proposed parallel algorithm of the coupled model is validated with one numerical example that confirm the consistent accuracy and applicability of the parallel algorithm by considerable time saving for large-scale problems

A time-domain approach for the simulation of three-dimensional seismic wave propagation using the scaled boundary finite element method

A direct time-domain approach to simulate seismic wave propagation in three-dimensional unbounded media is proposed based on the Scaled Boundary Finite Element Method (SBFEM). A domain of interest is commonly partitioned into a far field and a near field. The far field is modelled by the semi-analytical SBFEM satisfying rigorously the radiation conditions at infinity. Separate scaled boundary finite elements are employed to reach a balance between computational efficiency and accuracy. The near field is discretized into arbitrarily-shaped scaled boundary finite elements without the occurrence of hanging nodes. This advantage of the SBFEM in mesh generation is leveraged by incorporating the automatic octree-based meshing technique. By exploiting the geometrical similarity of both bounded and unbounded SBFE subdomains the computational cost is reduced. Inspired by the Domain Reduction Method (DRM), seismic waves are introduced to the system via a single layer of elements in the near field. This formulation of seismic input is mathematically convenient as it avoids the direct participation of the formulation of the far field. The proposed approach is attractive in a reliable simulation of the far field, flexible mesh generation of the near field and simple formulation of the seismic excitations. These merits are demonstrated through numerical simulations of seismic wave propagation in a free field and different examples featuring complex geometries in the near fields

Coupling Concept of two Parallel Research Codesfor Two and Three Dimensional Fluid Structure Interaction Analysis

This paper discuss a coupling strategy of two different software packages to provide fluid structure interaction (FSI) analysis. The basic idea is to combine the advantages of the two codes to create a powerful FSI solver for two and three dimensional analysis. The fluid part is computed by a program called PETSc-FEM a software developed at Centro de Investigacion de Metodos Computacionales CIMEC. The structural part of the coupled process is computed by the research code elementary Parallel Solver (ELPASO) of the Technische Universitat Braunschweig, Institut fur Konstruktionstechnik (IK).Fil: Garelli, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Schauer, Marco. Technische Universität Braunschweig; AlemaniaFil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Langer, Sabine C.. Technische Universität Braunschweig; Alemani

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

Seismische Risikoanalyse unterirdischer Versorgungsleitungen

Seismically caused failure of buried lifelines can result in disastrous events. Due to the grave consequences of those failures in past earthquakes, the need for reliable models examining the dynamic response of lifelines under earthquake excitation grows. In the present work, a methodology is developed to analyse the damage risk of buried lifelines exposed to seismic wave propagation. In order to perform this analysis, a three-dimensional numerical model is developed to describe the dynamic response of pipelines embedded in soil. Thereby, the emphasis is placed on three topics: the incorporation of dynamic soil-structure interaction, the advanced modelling of seismic excitation, and the over-all consideration of uncertainties. A hybrid finite element (FE)-scaled boundary finite element method (SBFEM) is presented to examine soil- structure interaction. Whereas the FEM enables a detailed modelling of the near-field, the SBFEM fulfils the wave radiation condition at infinity. In the latter method, increase of efficiency is, amongst others, achieved by employing substructuring techniques without losses of accuracy. For modelling seismic wave propagation in the near-field, a two-step procedure based on the domain reduction method is introduced. In the first step, a large scale simulation of the earthquake is performed, whereon the near- field is examined by the hybrid model. Thus, realistic seismic wave propagation inside the near-field can be modelled. Thereupon, an integrated probabilistic analysis is performed, which includes parameters of the entire seismic wave propagation path. For this process, a point estimate method is employed which enables an efficient and reliable determination of the failure probability of the pipeline. Parameter studies demonstrate the applicability of the present methodology which is not only applicable to lifelines but to any other structure under seismic wave excitation.Das seismisch bedingte Versagen von unterirdischen Versorgungsleitungen (Lifelines) und dessen Folgen offenbaren die Notwendigkeit von verlässlichen Modellen, die das dynamische Antwortverhalten realistisch abbilden. In der vorliegenden Arbeit wird eine Methode entwickelt, durch welche das Schadensrisiko von Lifelines infolge von seismischen Wellenausbreitungseffekten bestimmt werden kann. Zur Durchführung der Analyse wird ein dreidimensionales numerisches Modell entwickelt, welches das dynamische Verhalten von erdverlegten Rohrleitungen beschreibt. Bei der Entwicklung werden drei Schwerpunkte gesetzt: die detaillierte Abbildung der dynamischen Boden-Bauwerk-Wechselwirkung, die realistische Modellierung der seismischen Anregung sowie die globale Berücksichtigung von Unsicherheiten. Zur Untersuchung der Boden-Bauwerk-Wechselwirkung wird eine hybride Finite Element (FE)-Scaled Boundary Finite Element Methode (SBFEM) verwendet, wobei letztere die Wellenabstrahlung ins Unendliche simuliert. Effizienzsteigerungen können unter anderem durch den Einsatz von Substrukturmethoden erreicht werden. Zur Modellierung der seismischen Wellenausbreitung im Nahfeld wird eine Zwei-Schritt-Prozedur basierend auf der Domain Reduction Method vorgestellt. Im ersten Schritt wird eine großmaßstäbliche Simulation des Erdbebens durchführt, woraufhin im zweiten Schritt das Nahfeld mit der hybriden Methode untersucht wird. Diese Prozedur ermöglicht die Modellierung von realistischer seismischer Wellenausbreitung innerhalb des Nahfeldes. Darauf aufbauend wird eine ganzheitliche probabilistische Analyse durchgeführt, die Parameter des kompletten Ausbreitungspfades der seismischen Wellen einbindet. Für dieses Verfahren zur Ermittlung der Versagenswahrscheinlichkeit wird ein Punktschätzverfahren effizient eingesetzt. Parameterstudien zeigen die Anwendbarkeit der vorgestellten Methode, die sich nicht nur auf Rohrleitungen sondern auch auf jede andere Struktur unter seismischer Wellenbelastung erstreckt

Scaled boundary FEM :methodology development and applications for offshore wave diffraction

PhD ThesisMany offshore structures have been installed to harvest resources in the ocean. These large structures undergo several experimental and numerical tests before they are constructed. A reliable and efficient analysis tool is therefore crucial to this industry. Many methods have been introduced; each offering different advantages while providing the solution, as well as suffering from certain limitations. The scaled boundary finite element method (SBFEM) was developed to solve engineering problems. This particular method combines the advantages of two commonly used methods in the offshore industry, the Finite Element Method (FEM) and the Boundary Element Method (BEM), making it a suitable semi-analytical approach that requires less computational time while satisfying the boundary condition at infinity. Several attempts at using this method to solve the hydrodynamic problem have been executed with great success. However, there is still much room for further development. The first part of this thesis discusses further application of the two-dimensional SBFEM, using the proposed advantages by manipulating the position of the scaling centre to solve for more complex geometry. This methodology has also been extended with an integrated model to evaluate the wave-structure-soil interaction examining offshore monopile deflection. The second part of this thesis develops a three-dimensional (3D) SBFEM model. General formulations in the Scaled Boundary coordinates for the 3D SBFEM model have been developed and are presented in detail. Case studies have been carried out demonstrating the validity and efficiency of the 3D model. These developments are important in allowing extended usage of the methodology to solve more complex problems such as wave interaction with floating offshore structures. Due to its clear advantages in computational efficiency and accuracy, the extended SBFEM model can be applied to engineering problems in hydrodynamic analysis for more complex wave-structure interaction in the offshore industry

Seismic Analysis of Post-tensioned Gravity Dams using Scaled Boundary Finite Element Method

Dams are hydraulic structures built across rivers to create reservoirs, which provide essential services to society such as flood control, human water supply, and electricity generation. A dam shall be designed to ensure stability against overturning and sliding caused by the hydro-pressure of the reservoir. A common type of dam is the concrete gravity dam that mainly relies on its self-weight and resistance to sliding on the foundation to maintain its stability. Installing post-tensioned anchors (PTAs) is a practical and cost-effective technique in dam engineering. It provides an additional stabilizing force and improves the shear resistance at the dam-foundation interface. Seismic safety evaluation of post-tensioned concrete gravity dams is necessary for new dam designs or strengthened existing dams to guarantee that the structures will survive at specified seismic hazard levels. This thesis presents the development of an efficient numerical framework for the seismic analysis of post-tensioned concrete gravity dam-reservoir-foundation systems. This framework is realized by implementing the scaled boundary finite element method (SBFEM) in the well-known commercial FEM software ABAQUS as user elements (UEL). Polytope elements (polygonal elements in 2D and polyhedral elements in 3D) are as versatile as standard FEM solid elements, while they provide greater flexibility in mesh generation for bounded domains. Unbounded user elements (UEL) are derived to model wave propagation in far-fields. An unbounded UEL only requires discretization with a small number of faces at the near-field/far-field interface and can rigorously satisfy the radiation condition at infinity. The ABAQUS software enhanced with the UELs is employed for two-dimensional seismic analysis of gravity dams, overcoming the difficulties encountered in standard FEM, for example, local mesh refinement for geometrical features, generating matching interfacial meshes for weak joints, and simulation of anchor-structure interactions. The overall system consists of a near-field containing the dam body and its neighboring reservoir and foundation, and a far-field of the reservoir and foundation continua. The near-field dam and foundation are discretized as quadtree meshes assigned with polygonal UELs. Quadtree meshes allow rapid and smooth transitions in element size, which facilitates the local mesh refinement for dam lift joints, anchor boreholes, drainage systems, etc. An unbounded UEL represents the far-field foundation in terms of displacement unit-impulse response matrices. It captures free-field motions and transfers them as equivalent seismic inputs acting at the near-field/far-field interface. The reservoir is modeled by ABAQUS built-in acoustic elements. At the far end of the reservoir, a non-reflecting acoustic boundary embedded in ABAQUS is employed to satisfy the radiation condition of the unbounded reservoir. Comprehensive considerations have been taken in the numeral simulation of post-tensioned gravity dams, such as weak joint behaviors, anchor-structure interaction, and concrete damage. Weak joints in a concrete gravity dam, such as the dam-foundation interface and the dam lift joints, are the most likely places where the sliding and cracking occur. A cohesive-frictional contact scheme is utilized to simulate the non-linear behaviors of these weak joints. A PTA is usually grouted with the structure along a portion of the length, called bond length. At the grouting interface, the bond stress develops with the slippage between the anchor and structure, and then transfers the prestressing in the anchor to the structure. Cohesive elements connected with the anchor and structure are generated along the bond length to simulate the bond-slip interaction. A Mazars' damage evolution law for dynamic loading is applied to simulate the quasi-brittle behaviors of the concrete. To avoid mesh sensitivity, a partially regularized local damage model is introduced into this application. Automatic re-meshing algorithms to generate conforming interfacial meshes are developed for the sake of the simulation of interfacial problems. For the weak joints, the domains in contact are allowed to be discretized individually, and then the existing meshes at the interfaces are re-meshed to be node-to-node matching. The anchor is embedded automatically in the structure by inserting additional nodes into the existing structural meshes along the anchor layout. By duplicating the inserted nodes and connecting the duplicated nodes, beam elements conforming with structural meshes are formed naturally. These re-meshing procedures are easily operated on the polygonal meshes allowing arbitrary numbers of nodes and edges. Cohesive elements can be generated with the matching nodes at interfaces, and no constraints are required to connect them with the surrounding elements. The proposed approach is verified by performing seismic analysis of a post-tensioned gravity dam with simple geometry, and comparing the results obtained from the model using ABAQUS built-in elements. The advantages of the proposed approach in handling complex problems are demonstrated through dams with multiple inclined anchors. Applications of this method can be extended to three-dimensional cases, and composite materials with randomly spread fiber inclusions

High-performance computing for impact-induced fracture analysis exploiting octree mesh patterns

The impact-induced fracture analysis has a wide range of engineering and defence applications, including aerospace, manufacturing and construction. An accurate simulation of impact events often requires modelling large-scale complex geometries along with dynamic stress waves and damage propagation. To perform such simulations in a timely manner, a highly efficient and scalable computational framework is necessary. This thesis aims to develop a high-performance computational framework for analysing large-scale structural problems pertaining to impact-induced fracture events. A hierarchical grid-based mesh containing octree cells is utilised for discretising the problem domain. The scaled boundary finite element method (SBFEM) is employed, which can efficiently handle the octree cells by eliminating the hanging node issues. The octree-mesh is used in balanced form with a limited number of octree cell patterns. The master element matrices of each pattern are pre-computed while the storage of the individual element matrices is avoided leading to a significant reduction in memory requirements, especially for large-scale models. Further, the advantages of octree cells are leveraged by automatic mesh generation and local refinement process, which enables efficient pre-processing of models with complex geometries. To handle the matrix operations associated with large-scale simulation, a pattern-by-pattern (PBP) approach is proposed. In this technique, the octree-patterns are exploited to recast a majority of the computational work into pattern-level dense matrix operations. This avoids global matrix assembly, allows better cache utilisation, and aids the associated memory-bandwidth limited computations, resulting in significant performance gains in matrix operations. The PBP approach also supports large-scale parallelism. In this work, the parallel computation is carried out using the mesh-partitioning strategy and implemented using the message passing technique. It is shown that the developed solvers can simulate large-scale and complex structural problems, e.g. delamination/fracture in sandwich panels with approximately a billion unknowns (or DOFs). A massive scaling can be achieved with more than ten thousand cores in a distributed computing environment, which reduces the computation time from months (on a single core) to a few minutes