Topology optimization of continua considering mass and inertia characteristics

The center of mass and the inertia tensor are important parameters characterizing the kinetic properties of many structural systems, e.g., the rotor, spacecraft, and aircraft. In these occasions, designs not consistent with the requirements on the center of mass and inertia tensor cannot be accepted. In this paper, mathematical models are established to carry out the topology optimization of continua considering the mass and inertia characteristics. Two numerical examples, one for minimizing the static compliance considering locations of the center of mass and the other for maximizing the fundamental eigenfrequency considering both locations of the center of mass and values of the inertia products, are presented to demonstrate that the requirements on mass and inertia characteristics could have a profound influence on the final optimized layouts in structural topology optimization problems. On the other hand, the mass and inertia characteristics can also be tuned by topology optimization methods. In the second numerical problem, the smooth minimum operator is used to approximate the fundamental eigenfrequency with the first 4 eigenfrequencies so that the possible non-differentiability of the repeated eigenfrequencies can be avoided. Due to its extreme importance in engineering practice, the work of this paper can be useful to carry out designs in accordance with the requirements on the mass and inertia characteristics under the framework of traditional density-based structural topology optimization methods.