Title: Self-supporting Topology Optimization for Additive Manufacturing,
Abstract: The paper presents a topology optimization approach that designs an optimal
structure, called a self-supporting structure, which is ready to be fabricated
via additive manufacturing without the usage of additional support structures.
Such supports in general have to be created during the fabricating process so
that the primary object can be manufactured layer by layer without collapse,
which is very time-consuming and waste of material.
The proposed approach resolves this problem by formulating the
self-supporting requirements as a novel explicit quadratic continuous
constraint in the topology optimization problem, or specifically, requiring the
number of unsupported elements (in terms of the sum of squares of their
densities) to be zero. Benefiting form such novel formulations, computing
sensitivity of the self-supporting constraint with respect to the design
density is straightforward, which otherwise would require lots of research
efforts in general topology optimization studies. The derived sensitivity for
each element is only linearly dependent on its sole density, which, different
from previous layer-based sensitivities, consequently allows for a parallel
implementation and possible higher convergence rate. In addition, a discrete
convolution operator is also designed to detect the unsupported elements as
involved in each step of optimization iteration, and improves the detection
process 100 times as compared with simply enumerating these elements. The
approach works for cases of general overhang angle, or general domain, and
produces an optimized structures, and their associated optimal compliance, very
close to that of the reference structure obtained without considering the
self-supporting constraint, as demonstrated by extensive 2D and 3D benchmark
examples.