Lumped Mass Modeling for Local-Mode-Suppressed Element Connectivity Parameterized Topology Optimization of Vibrating Structures

For successful topology design optimization of crashworthy “continuum ” structures, unstable element-free and local vibration modefree transient nonlinear analyses should be ensured. Among these two issues, element instability was shown to be overcome if a recently-developed formulation, the element connectivity parameterization (ECP) is employed. On the way to the ultimate crashworthy structure optimization, we are now developing a local mode-free topology optimization formulation that can be implemented in the ECP method. In fact, the local mode-freeing strategy developed here can be also used directly for the standard element density method. Local modes are artificial, numerical modes resulting from the intrinsic modeling technique of the topology optimization method. Even with existing local mode controlling techniques, the convergence of the topology optimization of vibrating structures, especially experiencing large structural changes, appears to be still poor. In ECP, the nodes of the domaindiscretizing elements are connected by zero-length one-dimensional elastic links having varying stiffness. For computationally efficiency analysis for dynamic problems, every elastic link is now assumed to have two lumped masses at its ends. Choosing appropriate penalization functions for lumped mass and link stiffness is important for local mode-free results. However, unless the objective and constraint functions are carefully selected, it is difficult to obtain clear black-and-white results. It is shown that th