Developing BESO Topology Optimization Algorithm of Continuum Structures for Stiffness and Fundamental Frequency Considering Geometrical Symmetry Constraint

Topology optimization of structures, seeking the best distribution of mass in the design space to improve the performance and weight of a structure, is one of the most comprehensive issues raised in the field of structural optimization. In addition to the structure stiffness as the most common objective function, frequency optimization is of great importance in industries achieved by maximizing the fundamental frequency or the gap between two consecutive eigenfrequencies. The phenomenon of multiple frequencies, mesh dependency of topology responses, checkerboarding, geometric symmetry constraint, and occurrence of artificial localized vibration modes in low density regions are the most important challenges faced by the designer in stiffness and frequency optimization problems which influence the manufacturability of the design too. In this paper, BESO method is applied for a frequency and stiffness problem separately via creating a software package including a Matlab code and Abaqus FE solver. Also, in this paper the effect of geometric symmetry constraint is considered on resulted topologies from stiffness and frequency problems. So the BESO method is applied for modeling a 2D beam and its stiffness and frequency optimization and finally the optimization results of both objective functions will be compared with initial structure.