Summary: To solve generalized shape optimization problems, material topology optimization is applied to determine the basic layout, i.e., to insert and eliminate holes in the design space. In addition, the inner and outer contours are optimized in detail by shape optimization. To improve the quality of the results and to increase the numerical efficiency, the design model is adapted during the optimization process. Two aspects of design adaptivity are considered. On the one hand, the parametrization of the design space is varied during the material topology optimization process and, on the other hand, the kind of design model is adapted during the overall optimization process switching between material topology and shape optimization. The adaptive techniques are discussed, and adaptive design modeling is verified for topology optimization of shell structures.