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 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 interpolation in conjunction with the three-field density representation technique (original, filtered and projected design fields) is employed to achieve optimized solutions close to 0-1. Thus, parasitic effects of low-stiffness elements are circumvented. The mass density of each element is interpolated via a smooth Heaviside function yielding continuous transition between solid and void states of elements. This helps formulate a constraint on the maximum magnitude of the self-weight for the given volume in a such a manner that which implicitly imposes a lower bound on the permitted volume. The propose approach maintains the constrained nature of the optimization problem. Load sensitivities are evaluated using the adjoint-variable method. Compliance of the domain is minimized to achieve the optimized designs using the Method of Moving Asymptotes. Efficacy and robustness of the presented approach is demonstrated by designing various 2D and 3D structures involving self-weight.