Topology optimization of 2D trussed structures

Flavio A. C. Martins¹; Marcelo Araujo¹; Reyolando Brasil¹

¹ Universidade Federal do ABC

doi:10.20906/CPS/CILAMCE2017-0035

Resumo

In this work an optimization process in applied on a 2D truss subjected to static external forces and its self-weight. The objective of the optimization is minimizing the structure's weight in two steps: finding the minimum cross-section area for each bar element that is able to resist the internal loads. Constraints are considered on the maximum normal stress. In this first part it is used the Simplex method; and in a second step, in which an algorithm is created in order to shift the structure's nodes, finding a new topology that eliminates bar elements and searches for an optimal geometry to resist to the load, i.e., finding the minimum weight and optimum topology of a truss structure subjected to constraints in both normal stress and buckling effects. The sequence of nodes that are shifted in the process is made manually, while the algorithm determines when stop shifting one node, based on the gradient vector of the constraints' curves. For the optimization of the cross-section area, a new methodology for writing and defining the objective function based on the linearity of the system is proposed.

Palavras-chave: Topology optimization; buckling; trussed structures; discrete optimization; aerospace structures