基于子结构的内力约束连续体拓扑优化

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

通过拓扑优化可以得到传力路径,不同传力路径对应不同内力载荷.如果将内力载荷作为目标或约束进行拓扑优化,可以得到满足不同需求的传力路径,为拓扑优化的发展提供新思路和新方法.为了得到不同内力载荷需求的传力路径,基于子结构法将结构分开使内力暴露出来.以结构质量最小为目标,以内力为约束建立拓扑优化模型,基于独立、连续、映射(independent,continuous,mapping,ICM)方法和单位载荷法将内力显式化,通过累加获得需要控制的传力路径上的内力,通过迭代调整2个路径上的内力使其比值达到一个稳定的值,从而获得满足内力约束的传力路径.算例表明:不同的内力约束可以得到不同的传力路径.

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.