Topology optimization of stiff structures under self-weight for given volume using a smooth Heaviside function

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