Computational Bar Size Optimization of Single Layer Dome Structures Considering Axial Stress and Shape Disturbance

A computational method is proposed in this paper to minimize the material usage in the construction of modern spatial frame structures by prestressing a minimal number of members. The computational optimization is conducted in two steps. Firstly, a numerical model of a single-layer dome structure is used to minimize the cross-sectional area through several iterations. Different assumed ratios (r) ranging from 0.95 to 0.75 are multiplied by the designed cross-sectional area, and the optimal actual ratio (R) is determined through multiple steps using MATLAB. The selection of the optimum ratio is based on ensuring structural stability and considering various constraints. Secondly, a computational optimization is performed using the fmincon function in MATLAB, which employs an interior-point optimization algorithm to search for the minimum summation of the function. The algorithm is designed to exclude actuators with negligible actuation, thereby minimizing the number of actuators. Constraints are set on the stress of all members and the nodal displacements to maintain the desirable shape of the optimized structure. The obtained results demonstrate that the cross-sectional area of the numerical dome structure can be reduced by up to 18% by prestressing only nine members. The validity of the results is confirmed by comparing them with those obtained from MATLAB and SAP2000 software.