Extensions to the Growth Method of Size, Geometry and Topology Optimization of Truss Structures

Various design optimization methods for trusses layouts have been developed to find the optimum truss layouts. In most of these designing methods, topology optimization has been employed to find the optimum structures. Growth methods were developed to produce the optimal design of trusses based on the organism's evolution. These methods combine the topology and geometry optimization with a growth procedure to evolve the minimal connected and stable structure to an optimum one that satisfies the applied load and imposed constraints.
The sequential growth method was developed to find the optimum truss layout in a sequential manner by adding new joints and bars, requiring five steps: 1) domain specification; 2) topology and size optimization; 3) geometry optimization; 4) optimality verification, and 5) topology growth. This method was able to find the optimum trusses layouts efficiently. However, it was limited to single load case problems with stress and size constraints.
In this thesis, the sequential growth method for size, topology, and geometry optimization of truss structures were extended to incorporate multiple constraints such as stress and buckling, non-rectangular design domains, and multiple load cases. The five sequential steps were employed with modifications in the applied procedures of the topology optimization, the geometry optimization and the topology growth to carry out this extension. The finite element method for truss elements was implemented in MATLAB to analyze the structures during the optimization process. The MATLAB optimization toolbox was used to solve the numerical optimization problem and find the optimum trusses layouts. The optimization solver used the finite differences method to evaluate the derivatives of the objective function and the constraints with respect to the design variables.
The obtained results showed that the extended sequential growth method is able to find the optimum trusses layouts for different types of constraints and design domains. Several examples from the literature were used to demonstrate the efficiency of the extended sequential growth method.