Optimal collapse simulator for three-dimensional structures
Document typeMinor thesis
Rights accessOpen Access
In this project limit analysis for 3D structures is studied. The goal is to obtain for a certain structure the load factor that applied to the external loads induces collapse to the structure. The static theorem of limit analysis is the theoretical basis for the Structural Collapse Simulator (SCS), that is nding a stress distribution in equilibrium that does not violate yield criteria anywhere. This theorem is employed combined with linear programming techniques. Thereby a tutorial on LP problems is presented rst. Then a brief summary of the progresses in study of limit analysis for structures is o ered, being a useful introduction for understanding the very nature of SCS functioning. Moreover, limit analysis is developed and written as a LP problem, which consists of the maximization of the collapse load factor subject to equilibrium and yield criteria. Two major contributions are presented for nding the collapse load. Firstly, the yield curve of standard 2D beam cross sections is adaptively approximated with inscribed and circumscribed polygons that yield to lower and upper bounds of respectively. Secondly, an interesting approach for accounting with uniform distributed loads is shown, producing bounding of the load factor. Combining these two techniques the bound gap can be reduced arbitrarily, observing convergence of the upper and the lower bounds to the exact load factor. A tutorial for using SCS and computing structures is provided, and numerical examples are thoroughly studied in order to illustrate the functioning of the program and the limits of the method. Finally, recent developments and future branches of research are detailed in order to widen the applicability range of SCS, the most important being the adaptive approximation of the yield surface for 3D beams.