Gradient-Based Truss Topology Optimization with Local Stress and Buckling Constraints Considering Chain Effects - Eugénio, Luís Pedro Abelha (2022)
In this dissertation, a gradient-based optimization, utilizing both MMA and GCMMA optimization algorithms, is applied to a truss topology optimization problem including local stress and buckling constraints. The problems with these constraints are prone to be affected by the singularity phenomenon where the global optimum is in a degenerated region of the design domain. This can prevent the elimination of bars when their areas tend to zero because the stress/buckling constraints are violated. Through a combination of relaxation techniques, namely ε-relaxation, a continuation approach and an adaptation of the constraint's formula- tion, the singularity phenomenon can be overcome. The known chain effect in truss topology optimization is addressed by implementing a reverse SIMP function that is used to smooth out the "jump" in the buckling length. This buckling length correction is thus performed in the continuum set of the problem design variables which allows the use of gradient-based algo- rithms. The developed methodology is firstly tested resorting to a set of problems with analyti- cal solutions. Then the proposed algorithm is applied to a new set of complementary examples increasing the number of bar elements. The results found by the MMA optimization algorithm represent reliable solutions that prove the efficiency of the proposed formulation to deal with buckling constraints. Finally, the GCMMA's results agreed with the MMA results in all but two examples, where it showed some difficulties in escaping from local minimum.