Structural Topology Optimization Considering The Overhang Constraint In Additive Manufacturing

It's relatively easy to fabricate highly complex structures by additive manufacturing technology,which is subversive and provides wide design space for structural designers,while the traditional structural design methods can't take full advantage of the application potential of additive manufacturing.Then,topology optimization methods with high freedom of design are efficient and advanced,and we are able to design structures,which is hard to fabricate by traditional manufacture process,with excellent performance and novel geometric configuration by topology optimization methods.Naturally,there is a trend to combine additive manufacturing technology and topology optimization methods.In the structural topology optimization towards additive manufacturing technology,it's of necessity to consider the unique additive manufacturing constraints,such as overhang constraint studied in this paper.The overhang constraint means that the inclination angles of structural downward-facing boundaries must be larger than a specified angle.In this paper,self-supporting structures will be designed by considering the overhang constraint,which can prevent the structure from warping or collapsing and reduce the use of support material as well as printing time during some additive manufacturing process.In the framework of level set topology optimization method,this paper extracts the normal vector of structural boundary and make use of the dot product of normal vector and printing direction to detect boundary that violate the overhang constraint.Based on the characteristic of signed distance function,the point-wise overhang constraint is written equivalently as a single domain integral and a single boundary integral.Through detailed theoretical derivation and numerical example with various overhang constraints and different printing directions,it's seen that two kinds of method dealing with the overhang constraint are effective and self-supporting structures can be obtained from an initial design violating the overhang constraint.