Topology Optimization for Continuous Structures With Internal Force Constraints Based on the Substructure

The loading paths can be obtained with the topology optimization and different loading paths are related to different internal forces. Taking the internal forces as the object or constraint, the loading paths can be obtained to meet the various demands with the topology optimization, which provides new ideas and new methods for the development of topology optimization research. To obtain the loading paths with different internal force requirements, the structures can be separated to expose the internal forces based on substructure method. A topology optimization model was established to minimize the weight with internal force as constraint. The internal force was explicit with the independent, continuous, mapping (ICM) method and the unit load method. The internal forces were added to get the total internal force on the controlled loading paths. The ratio of the internal forces on two loading paths reached a stable value by iteration to obtain the loading path meeting the internal force constraint. The numerical examples show that different loading paths can be obtained with different internal force constraints.