Automatic generation of truss models for the optimal design of reinforced concrete structures

The truss model approach is evolving as one of the most useful design methods for shear critical structures and for other disturbed regions in concrete structures. In practice, two situations may arise: either the structure is sufficiently complex to preclude finding a reasonable truss, or, several trusses can be introduced to the same structure albeit without a clear selection mechanism as to which is the "best". In fact, even the word "best" does not have a clear meaning as per the existing literature. This constitutes a fundamental obstacle to the truss model approach and may limit its future usefulness.;The strategy of this thesis can be summarized as follows: (1) To understand the underlying physics (first part of chapter 2) resulting in characterizing the objective functions that should be met in the design of reinforced concrete structures. The solution domain used here is still continuous (a continuum), therefore, it is natural for such a study to be dominated by continuum mechanics. (2) To rationalize an approximate method (truss models) for discretizing the continuum. This constitutes the second part of chapter 2 in which methods such as perturbation theory are employed. (3) To develop algorithms for treating the resulting discrete problem (chapters 4 and 5). Now the treated problem is discrete and theoretical computer science takes over. The numerical problem has challenging aspects because of the non-smooth objective functions associated with the design goals set in 1 above. (4) To produce a toolbox that enables the user to apply all the above concepts (appendix A). Although the toolbox and its supporting software (Matlab;Except for chapter 3 (which is a more accurate version of chapters 2 and 4), the above steps are in the same order as the chapters of this thesis, which is intentionally the same as the logical order for addressing problems in science and engineering.