The thesis introduces a generalized modelling and higher-order accurate analysis of curved shells and structural membranes. The classical shell and membrane models which describe the physical behaviour of thin-walled structures are reformulated in the frame of the tangential differential calculus. The major advantages of the reformulation are a more compact notation independently of the employed geometry definition and recent finite element methods (FEM) are applicable. The recast models are descritized on explicitly and implicitly defined geometries with standard FEM (Surface FEM) and recent fictitious domain methods (Trace FEM) with higher-order accuracy. Provided that the involved mechanical fields are sufficiently smooth, optimal orders of convergence are achieved for linear shells and non-linear membranes in the Surface and Trace FEM.weiterlesen