Structural topology optimization subject to overhang angle constraint with overhang length relaxation in additive manufacturing

This paper studies additive manufacturing(AM) oriented structural topology optimization(TO).The minimum compliance design subject to overhang angle constraint with overhang length relaxation and horizontal minimum length control is considered.Although the overhang length relaxation allows additional flexibility for AM product design,there have been very limited studies on it.This paper elucidates that the overhang angle constraint we proposed can identify the lower boundary element that violates the overhang angle constraint.Taking advantage of this fact,we achieve the overhang length relaxation by specifying that the volume fraction of the elements that violate the overhang angle constraint in each local area of the design domain is less than a specified upper bound.A formula for estimating the maximum allowable overhang length of this method is proposed and verified.The horizontal minimum length constraint is also employed in this paper.While controlling the horizontal length size of the structural member,this constraint together with the overhang angle constraint with overhang length relaxation suppresses the hanging feature.The gradient-based optimization algorithm method of moving asymptotic(MMA) is used to solve the TO formulation.Numerical examples show the effectiveness of this method.It is observed that the new constraint alleviates the main issues of traditional overhang angle constraints,i.e.,gray element issue,stress concentration issue,and shattered structure issue.Compared with the strict traditional overhang angle constraint,the new formulation reduces structural compliance.