Truss Topology Optimization against Local Buckling Conditions

This project has reconsidered a truss topology optimization algorithm originated by Pedersen. The algorithm considers local buckling effects within each bar due to static equilibrium of the overall design. This results in a non-convex cost function. In this project this framework is extended to allow for ground structures and the effect of the restriction of the possible bars to non-convex design domains are investigated. In another branch of the project an important deficiency in previously developed methods to the local buckling problem is considered and a possible solution procedure is developed. Consider a bar in a generated design and add a node to the internal part of this bar. Due to the non-linearity and concavity of the objective function, the cost of the two small bars is lower than the cost of the long bar. In this case, the bar should be considered as one long bar. However, if a third bar is added connecting to the internal node, the long bar should be modelled as two short bars. An objective evaluation has been implemented evaluating the correct design cost in these situations. The concept of chains as a generalization of bars, to line segments with two or more spanning nodes, is introduced. Moreover, indexing of designs as a simple count of the number of bars in the design connecting to each node is considered. Despite its simplicity design indices allows for efficient localization of critical nodes. From the point of view of static equilibrium the critical nodes are the nodes where the constraining force equilibrium matrix displays linear dependencies.