Structural topology optimization based on system condensation

• We present the topology optimization scheme combined with the system reduction.
• Design sensitivity based on the reduction system is evaluated.
• Proposed topology optimization scheme includes the mode tracking method.

Topology optimization problem requires repeated evaluations of the objective function and design sensitivity in the design domain with various density distributions. A repeated computations in the optimization process, requires a large amount of computing time and resources. These issues have inspired the development of optimization techniques combined with a system reduction. In order to reduce the system, this study employs a system dynamic condensation method based on selected primary degrees of freedom. Based on a system reduction, this study performs a topology optimization to maximize the eigenvalue and linear summation of each eigenvalue. In the optimization procedure, mode tracking method, called MAC, is used to pursue target modes, and the design sensitivity is calculated by a method of the rigid body mode separation assuring the reliability of sensitivity regardless of the design variable perturbation size. Each result of the numerical examples based on the reduction system is compared to that of the full system. Through a few numerical examples, it is demonstrated that the proposed method can provide efficient and reliable results in topology optimization.