  This paper presents a density-based topology optimization approach to design
structures under self-weight load. Such loads change their magnitude and/or
location as the topology optimization advances and pose several unique
challenges, e.g., non-monotonous behavior of compliance objective, parasitic
effects of the low-stiffness elements, and unconstrained nature of the
problems. The modified SIMP material scheme is employed with the three-field
density representation technique (original, filtered, and projected design
fields) to achieve optimized solutions~close~to~0-1. A novel mass density
interpolation strategy is proposed using a smooth Heaviside function, which
provides a continuous transition between solid and void states of elements and
facilitates tuning of the non-monotonous behavior of the objective. A
constraint that implicitly imposes a lower bound on the permitted volume is
conceptualized using the maximum permitted mass and the current mass of the
evolving design. Sensitivities of the objective and self-weight are evaluated
using the adjoint-variable method. Compliance of the domain is minimized to
achieve the optimized designs using the Method of Moving Asymptotes. The
Efficacy and robustness of the presented approach are demonstrated by designing
various 2D and 3D structures involving self-weight. The proposed approach
maintains the constrained nature of the optimization problems and provides
smooth and rapid objective convergence.
