A smooth integration of geometric models and numerical simulation has been in the focus of research in computational mechanics for long, as the classical transition from CAD-based geometric models to finite element meshes is, despite all support by sophisticated preprocessors, very often still error prone and time consuming. High-order finite element methods bear some advantages for a closer coupling, as much more complex surface types can be represented by p-elements than by the classical low order approach [1]. Significant progress in the direction of model integration has recently been made with the introduction of the isogeometric analysis concept [2], where the discretisation of surfaces and the Ansatz for the shape functions is based on a common concept of a NURBS-description. In this paper we discuss a recently proposed different approach, the Finite Cell Method (FCM) [3], which combines ideas from meshless and embedded domain methods with high-order approximation techniques. The basic idea is an extension of a partial differential equation beyond the physical domain of computation up to the boundaries of an embedding domain, which can easier be meshed. The actual domain is only taken into account using a precise integration technique of cells which are cut by the domains boundary. If this extension is smooth, the solution can be well approximated by high-order polynomials. The method shows exponential rate of convergence for smooth problems and good accuracy even in the presence of singularities. The formulation in this paper is applied to linear elasticity in two and three dimensions, although the concepts are generally valid. The method seems to be especially promising for domains of very complex shape or very inhomogeneous material distribution, which arise e.g. from CT-scans of human bone. Whereas generation of flawless meshes may take hours, an FCM grid can be generated within seconds. Numerical results are presented and compared to finite element results with respect to accuracy, computational resources and engineering effort for data preparation.
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A smooth integration of geometric models and numerical simulation has been in the focus of research in computational mechanics for long, as the classical transition from CAD-based geometric models to finite element meshes is, despite all support by sophisticated preprocessors, very often still error prone and time consuming. High-order finite element methods bear some advantages for a closer coupling, as much more complex surface types can be represented by p-elements than by the classical low o...
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