Mac-based mode-tracking in structural topology optimization

An efficient mode-tracking method based on the modal assurance criterion (MAC) is formulated for the structural topology optimization of maximizing the eigenfrequencies of desired modes. The present method is very effective in tracing each of the desired modes correctly even when the structural topology and shape, change substantially from the initial configuration. The use of MAC eliminates the need for mass orthogonalization and the use of selected nodal data enhances numerical efficiency greatly. The penalized density function approach for topology optimization allows an interesting interpretation in the sensitivity analysis. The use of an explicit penalty function in the objective function is proposed, which helps suppress undesirable intermediate densities.