Global shape optimization of free-form cable-stiffened latticed shell based on local optimal solutions

•A modified shape optimization method of cable-stiffened latticed shell is proposed to avoid the non-smooth solutions.•Weight sum method is employed to solve the modified equation.•Smooth solutions can be obtained with suitable weights.•A variable weight method based on modified equation is proposed to achieve the global optimal shape. In the present work, local optimal solutions in shape optimization of cable-stiffened latticed shells are discussed and a modified optimization method is presented. Firstly, a shape optimization method is used to minimize the strain energy of different kinds of cable-stiffened shells. It can be confirmed that local optimal solutions exist in this shape optimization problem. Secondly, in order to get smooth solutions, this paper puts forward a modified optimization method, in which total length of members or smoothness parameter is employed as a correction term in the optimization equation. In this approach, the modified equation can be solved by weight sum method. The results indicate that smooth optimal solutions can be obtained by solving this equation. Finally, a variable weight method is proposed to achieve the global optimal shape from any initial shape in one-step optimization. In this approach, the weight changes along with the iteration process. The results illustrate that this method is efficient and the global optimal shape is achieved successfully.