Truss Topology Optimization Based on a Birth/Death Element Approach

In this paper, an alternative approach for topology optimization of truss-type structures is presented. The structural design is translated to a constrained discrete optimization problem based on weight reduction, with performance considerations included in its objective function. The constraints are related to the maximum global stress and to the individual strain energy density. Each member has a standard profile and its absence/presence in the structural representation is implemented with a binary coding; in order to avoid singularities while in the structural analysis, a scheme for simulating the effects of missing members by means of the birth/death element technique is applied. An energy-based approach is employed to detect those elements that not contribute to the overall stiffness. The optimization problem is solved by applying a Modified Binary Differential Evolution algorithm, and the graph theory is applied in parallel with the optimization process to discard unfeasible structures and reduce execution time. The structural performance is evaluated by an execution-time static analysis based on the finite-element method, considering the behavior in a 3-D environment and using commercial software to reduce the uncertainty in this step. The presented proposal is implemented in ANSYS APDL, using as case studies two different structures with a specific load case. The obtained results show a volume reduction of more than 40% off the initial structures, indicating that the proposed approach can be a high-quality tool for structural design in real engineering problems.