  Additive manufacturing is a free-form manufacturing technique in which parts
are built in a layer-by-layer manner. Laser powder bed fusion is one of the
popular techniques used to fabricate metal parts. However, it induces residual
stress and distortion during fabrication that adversely affects the mechanical
properties and dimensional accuracy of the manufactured parts. Therefore,
predicting and avoiding the residual stress and distortion are critical issues.
In this study, we propose a topology optimization method that accounts for the
distortion. First, we propose a computationally inexpensive analytical model
for additive manufacturing that uses laser powder bed fusion and formulated an
optimization problem. Next, we approximate the topological derivative of the
objective function using an adjoint variable method that is then utilized to
update the level set function via a time evolutionary reaction-diffusion
equation. Finally, the validity and effectiveness of the proposed optimization
method was established using two-dimensional design examples.
