|M.Sc Student||Zelickman Yakov|
|Subject||Topology optimization with strees constraints using material|
|Department||Department of Civil and Environmental Engineering||Supervisor||Professor Oded Amir|
|Full Thesis text|
In recent years topology optimization has become a widely used predesign tool for structural engineers from all disciplines. As so, more research is focused on industrial needs. One of the structural fundamental requirements is the integrity of the structures. As material failure is strongly related to stresses, these should remain in a predefined stress range, usually the yielding stress divided by a safety factor. Therefore it is beneficial to combine the stress limitations in the predesign procedure i.e. topology optimization.
Despite the obvious need, stress constraints are usually not imposed in the optimization problem formulation due to difficulties associated with them. The major difficulty is related to the local nature of the stresses that makes stress constraints extremely costly in terms of computational time. Existing methods to reduce the computational cost suggest to use constraints in a modified manner, and either still have high computational cost or have weak control over the stresses.
In this research we suggest a different method that circumvents the difficulties rather than dealing with them straight-forwardly. The core of the method is the assumption that since structural optimization seeks for the stiffest structure with a given material amount, the obtained optimal structure will not have any damage as damaged material has reduced stiffness. Thus by appropriate selection of the damage model's parameters stresses can implicitly be constrained. In order to formulate the method, the damage model as well as the finite element implementation are first presented in detail. Then several optimization formulations are presented together with further considerations such as detailed interpolation schemes and length scale control. Because the analysis is path dependent, the sensitivity analysis is relatively complicated and therefore it is presented in detail. Three different benchmark problems are used to investigate the method's performance and capabilities. Eventually the numerical experiments provide encouraging results showing significant reduction of the stresses when the damage model is used.