SUMMARY

Enforcing essential boundary conditions plays a central role in immersed boundary methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints. We formulate an extension of Nitsche's method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the B-spline and non-uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries. Furthermore, we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3D geometries. With several benchmark problems, we demonstrate the overall good convergence behavior of the proposed method and its good accuracy. We provide extensive studies on the stability of the method, its influence parameters and numerical properties, and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two. A newly composed boundary integration concept further enhances the modeling process and allows a flexible, discretization-independent introduction of boundary conditions. Finally, we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non-uniform rational basis spline geometries. Copyright © 2013 John Wiley & Sons, Ltd.

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Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method

Multicast communications is an efficient mechanism for one-to-many transmissions over a broadcast wireless channel, and is considered as a key technology for supporting emerging broadband multimedia services in the next generation wireless networks, such as Internet Protocol Television (IPTV), mobile TV, etc. Therefore, it is critical to design efficient multicast scheduling schemes to support these multimedia services. In this paper, we propose a cooperative multicast scheduling scheme for achieving efficient and reliable multicast transmission in IEEE 802.16 based wireless metropolitan area networks (WMAN). By exploiting the multi-channel diversity across different multicast groups and user cooperation among group members, the proposed scheme can achieve higher throughput than existing multicast schemes, for subscriber stations in both good and bad channel conditions. In addition, it has good fairness performance by considering the normalized relative channel condition of each multicast group. An analytical model is developed to evaluate the performance of the proposed scheme, in terms of service probability, power consumption, and throughput of each group member and multicast groups. The efficiency of the proposed scheme and the accuracy of the analytical model are corroborated by extensive simulations.

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A cooperative multicast scheduling scheme for multimedia services in IEEE 802.16 networks

Standard methods for predicting bone's mechanical response from quantitative computer tomography (qCT) scans are mainly based on classical h-version finite element methods (FEMs). Due to the low-order polynomial approximation, the need for segmentation and the simplified approach to assign a constant material property to each element in h-FE models, these often compromise the accuracy and efficiency of h-FE solutions. Herein, a non-standard method, the finite cell method (FCM), is proposed for predicting the mechanical response of the human femur. The FCM is free of the above limitations associated with h-FEMs and is orders of magnitude more efficient, allowing its use in the setting of computational steering. This non-standard method applies a fictitious domain approach to simplify the modeling of a complex bone geometry obtained directly from a qCT scan and takes into consideration easily the heterogeneous material distribution of the various bone regions of the femur. The fundamental principles and properties of the FCM are briefly described in relation to bone analysis, providing a theoretical basis for the comparison with the p-FEM as a reference analysis and simulation method of high quality. Both p-FEM and FCM results are validated by comparison with an in vitro experiment on a fresh-frozen femur.

The finite cell method for bone simulations: verification and validation

Since the various people involved in the design process for a building project tend to hold conflicting views, this inevitably leads to a range of disparate models for planning and calculation purposes. In order to interpret the relevant geometrical, topological and semantical data for any given building model, we identify a structural component graph, a graph of room faces, a room graph and a relational object graph as aids and explain algorithms to derive these relations. We start with a building model by transferring its geometrical, topological and semantical data into a volume model, decomposing the latter into a so-called connection model and then extracting all air volume bodies and hulls of the model by means of further decomposition into elementary cyclic connection components. The technique is demonstrated within the scope of building energy simulation by deriving both a dimensionally reduced object model required for setting up a thermal multizone model and a geometrical model for defining single or multiple computational fluid dynamic domains in a building together with incidence matrices correlating these models. The algorithm is basically applicable to any building energy simulation tool.

Dimensional reduction of 3D building models using graph theory and its application in building energy simulation

Computer-aided design-based NURBS surfaces form the basis of isogeometric shell analysis which exploits the smoothness and higher continuity properties of NURBS to derive a suitable analysis model in an isoparametric sense. Equipped with higher order approximation capabilities the used NURBS functions focus increasingly on rotation-free shell elements which are considered to be difficult in the traditional finite element framework. The rotation-free formulation of shell elements is elegant and efficient but demands special care to enforce reliably essential translational and rotational boundary conditions which is even more challenging in the case of trimmed boundaries as common in CAD models. We propose a Nitsche-based extension of the Kirchhoff-Love theory to enforce weakly essential boundary conditions of the shell. We apply our method to trimmed and untrimmed NURBS structures and illustrate a good performance of the method with benchmark test models and a shell model from engineering practice. With an extension of the formulation to a weak enforcement of coupling constraints we are able to handle CAD-derived trimmed multi-patch NURBS models for thin shell structures.

Weak Dirichlet boundary conditions for trimmed thin isogeometric shells

Mathematical Foundations of Computational Engineering

Mathematische Grundlagen der Ingenieurinformatik

CITATION: Galishnikova, V., Dunaiski, P. & Pahl, P.J. 2009. Geometrically Nonlinear Analysis of Plane Trusses and Frames. Stellenbosch: SUN MeDIA. doi:10.18820/9781920109998.

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Geometrically nonlinear analysis of plane trusses and frames

The construction of Voronoi diagrams and Delaunay triangulations finds wide application in many branches of science. Delaunay triangulations have properties which make them more desirable than other triangulations for the same node set. Delaunay has characterized his triangulations by the empty circle property. The partitioning and flipping methods which have been developed for digital construction of Voronoi diagrams and Delaunay triangulations only make indirect use of this property. A novel method of construction is proposed, which is based directly on the empty circle property of Delaunay. The geometry of the steps of the algorithm is simple and can be grasped intuitively. The method can be applied to constrained triangulations, in which a triangulation domain and some of the edges are prescribed. A data structure for triangulations of concave and multiply-connected domains is presented which permits convenient specification of the constraints and the triangulation. The method is readily implemented, efficient and robust.

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Constrained Construction of Planar Delaunay Triangulations without Flipping

The effective buckling length of a column in a steel frame depends on the sidesway of the frame. The classification sidesway - no sidesway of a frame depends on all members of the frame and is made on an empirical basis. A change of class leads to large changes in the effective column length, and thus affects the buckling load and the economy of the column design. In order to avoid the uncertainties of the empirical classification, it is proposed to determine the buckling load of the complete frame with a nonlinear analysis. The method is illustrated with an unbraced and a braced frame, which are analyzed for hinged as well as fixed columns at ground floor level. The forces in the columns at buckling of the frames are compared to the buckling loads of the single columns. The design of high-rise steel frames against buckling by sidesway - no sidesway categorization has been compared to the buckling analysis of the frames as a whole with nonlinear models. The results confirm the large differences between the buckling loads of braced and unbraced high-rise frames, which are well known from analytical solutions for simple portal frames.

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Peter Jan Pahl

Papers

Mathematical Foundations of Computational Engineering

Mathematische Grundlagen der Ingenieurinformatik

Geometrically nonlinear analysis of plane trusses and frames

Constrained Construction of Planar Delaunay Triangulations without Flipping

Analysis of frame buckling without sidesway classification