Geometry Control Equation of the Circular Ring Tower Based on Unstressed State Amounts - Lixin Ou; Yi Liu; Qingfu Li; Xiyu Ma (Advances in Civil Engineering)
In high-degree-of–freedom complex structures, the ill-conditioning or singularity of the stiffness matrix is a key factor affecting the accuracy and stability of structural analysis. Regularization techniques are introduced to solve this issue. The introduction of a regularization parameter can effectively transform the stiffness matrix from a singular matrix to a nonsingular one, thus enabling stable matrix operations and avoiding numerical instability in traditional methods. In the case of a stay cable ring tower structure, finite element (FE) modeling was first used to analyze the forces and deformations of the structure during construction. After the model was established, a simulation analysis of the loads at different construction stages was conducted, and the deformation distribution at each node was obtained. To further optimize shape control, the regularization parameter was adjusted, and the shape of the structure in the unstressed state was calculated. After adjusting the regularization parameter, the calculated unstressed shape under external loads showed a better performance than the manufacturing shape. Specifically, it was found that when the regularization parameter η was between 1018 and 3 × 1018, the calculated unstressed shape could accurately control the structural deformation under load, with the maximum error controlled within 2 mm.