Optimization has become an important tool in engineering activities because it represents a systematic method to improve design with respect to certain criteria. Within the thesis a numeric-symbolic approach to limit load shape optimization is studied which enables the use of an optimization algorithm as an ultimate state design tool. Shape is parameterized symbolically using a general computer algebra system. Therefore the design velocity filed can be computed analytically and an exact sensitivity analysis can be carried out. Accurate sensitivity information is of crucial importance for proper gradient shape optimization. When analyzing imperfection sensitive structures it turns out that the choice of the shape and size of initial imperfections has a major influence on the response of the structure and its ultimate state. Further on, shape optimization applied on the perfect mathematical model can lead to non-optimal results, e.g. a very light structure but very sensitive to buckling. While imperfections are not known in advance, a method for direct determination of the most unfavorable imperfection of structures by means of ultimate limit states was developed. The method is implemented as an internal and separate optimization algorithm within the global shape optimization process. Full geometrical and material nonlinearity is considered throughout the global optimization process consistently, resulting in efficient and robust, ultimate limit load structure design algorithm. The numerical examples indicate that the use of a symbolic-numeric system for gradient shape optimization combined with the use of the most unfavorable imperfections can represent a superior alternative to conventional ultimate limit state design.
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