The Finite Cell Method is an immersed boundary method combined with higher order finite elements. In FCM, the material parameters of the fictitious domain are scaled down, thus a discontinuity is introduced in the cut finite cells. This introduces an error in the integrals of the stiffness matrix. Typically, composed Gaussian quadrature for evaluating integrals in the cut cells is used, based on a spacetree decomposition. The drawback of the spacetree decomposition is that it introduces a high number of quadrature points and yields only a 0 th order aproximation of the geometry. The thesis proposes a different apporach to deal with integration: the cut cells are decomposed into quadrilaterals and triangles with curved sides and the quadrature points are distributed on their parameter spaces. To this end, an algorithm is proposed that performs this decomposition in two dimensions. The algorithm is able to work on complex geometries. The results show that the blended subcell integration is able to produce results with higher precision yet still less integration points than the spacetree approach. Thus, the overall computational effort of FCM analyses is considerably reduced in comparison to the spacetree integration. This makes the proposed approach a good fit into the design-through-analysis pipeline.     «

The Finite Cell Method is an immersed boundary method combined with higher order finite elements. In FCM, the material parameters of the fictitious domain are scaled down, thus a discontinuity is introduced in the cut finite cells. This introduces an error in the integrals of the stiffness matrix. Typically, composed Gaussian quadrature for evaluating integrals in the cut cells is used, based on a spacetree decomposition. The drawback of the spacetree decomposition is that it introduces a high n...     »