An efficient and robust shape optimization framework for gridshell designs based on node shifting method

In this paper, a novel and efficient shape optimization framework for freeform gridshell designs, especially for cantilevering structures, is proposed based on the node shifting method. The nodal coordinates are directly chosen as the design variables without any extra parameterization, and are iteratively updated to minimize the structural compliance. The distributed load filter is introduced for a smoother and more efficient shape updating scheme, where the negative sensitivity numbers are applied as the virtual external load for the shape updating analysis to guarantee both the smoothness of surfaces and the sustained reduction of structural compliance at each step. The penalized volume adjustment subroutine is then applied to satisfy the volume constraint and to improve the uniformity of grids. Compared to the conventional nodal shifting methods, it is observed that a much more stable and faster convergence is achieved. A variety of examples are presented to demonstrate the improved effectiveness and the efficiency of the proposed algorithm.