Topology optimization of assembled structures by sequential density-based approach
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Structural optimization as well as on-site additive manufacturing as well as on-site assembly of large scale structures from preproduced segments, e.g. bridges and other buildings, became increasingly attractive in civil engineering. Common optimization approaches do not take into account the sequential manufacturing or assembly of those structures, i.e. the design of a structure is optimized as one closed geometry. To improve manufacturability and assembly of those structures, we introduce a sequential topology optimization approach in which the limited range of the manufacturing machine, e.g. a robot arm in additive manufacturing or crane, and/or size of preproduced segments is accounted for. In this sequential topology optimization approach, the design space is limited regarding to the reach of the manufacturing machine or segment size and is gradually increased, resulting in multiple separated production steps or optimized segments. Besides the structural weight, the weight of the manufacturing machine at its position during manufacturing or assembly of the next segment is applied. Thus, the optimization yields step by step new structural segments which are optimal to bear its weight for the given production step and the weight of the manufacturing machine during production of the next segment. For each segment, more material is allowed to be added during optimization but structural parts established during optimization of former segments is not allowed to be removed. This allows to extend the structure segment by segment without removing (supporting) structures from previous production steps. For the topology optimization, we apply the thermodynamic topology optimization approach. The thermodynamic topology optimization is based on Hamilton’s principle which yields a closed set of partial differential equations for the mechanical equilibrium and the optimization as well. The set of equations is solved in a staggered approach for maximum numerical efficiency: the balance of linear moment is solved by means of classical finite element method whereas the partial differential equation describing the evolution of the design variables towards the optimum are solved with a meshfree finite difference scheme. To this end, the thermodynamic topology optimization under self-weight is introduced and numerical examples for a two-dimensional, sequentially manufactured bridge for varying material- and manufacturing machine weights are presented.