基于单元过滤的自支撑结构拓扑优化方法

A Topology Optimization Method for Self-supporting Structures Based on Element Filtering

为了避免零部件在增材制造过程中使用支撑结构,基于单元过滤提出一种面向增材制造的自支撑结构拓扑优化方法。采用四节点矩形单元离散设计域建立悬垂特征有限元模型。模拟增材制造逐层堆积材料的成型过程,构建一种基于Heaviside函数的自支撑单元过滤法则,采用此法则逐层保留自支撑单元并删除非自支撑单元。基于固体各向同性材料惩罚模型(SIMP)变密度法,建立面向增材制造的自支撑结构拓扑优化模型,并采用移动渐近线法(MMA)求解此模型。将自支撑结构拓扑优化方法应用到三点弯曲简支梁(MBB)拓扑优化中。数值案例结果表明:与传统拓扑优化方法相比,自支撑结构拓扑优化方法能够在4个打印方向上对MBB梁进行优化设计,实现打印过程自支撑,并节省打印材料最多达20.6%,缩短打印时间最多达16.6%,解决了传统拓扑优化结构在增材制造过程中需要使用支撑的问题。

To avoid the use of support structures in the additive manufacturing process of components,this paper proposes an additive manufacturing oriented topology optimization method for self-supporting structures based on element filtering.By using 4-node rectangular element to discretize the design domain,a finite element model of overhang is established.A filtering rule of the self-supporting element based on Heaviside function is constructed by simulating the layer-by-layer forming process of additive manufacturing.The self-supporting elements are retained,and the non-self-supporting elements are deleted by this rule layer-by-layer.Based on the solid isotropic material with penalization(SIMP)model,the additive manufacturing oriented self-supporting structure topology optimization model is formulated,and the method of moving asymptotes is used to solve this optimization problem.The topology optimization method of self-supporting structures is applied to the topology optimization for the Messerschmidt-Bolkow-Blohm(MBB)beam.The results of case studies show that compared with the traditional topology optimization method,this method can achieve optimal design of self-supporting structure for the MBB beams along four printing directions,and moreover,the material and printing time can be saved up to 20.6%and 16.6%at most,respectively.It can solve the problem that traditional topology optimization structures need supports in additive manufacturing process.