A numerical strategy for relieving pretension of cable net structures by exchanging stiffness components. (15th March 2023) - Wang, Xintao; Deng, Hua; Fang, Weiding
Highlights: Deformation generated by dominant load is resisted by key structural stiffness. Relieve pretension but maintain key structural stiffness constant. Key structural stiffness is described in the eigen-space of tangent stiffness matrix. Reduced geometrical stiffness is compensated by enhancing elastic stiffness. Rehabilitate key structural stiffness by adjusting cross-sectional areas of cables. Abstract: Cable net structures are generally highly tensioned to resist the deformation induced by external loads, while the peripheral structural members are heavily burdened to balance the pretension. A numerical strategy is proposed to relieve the pretension without changing the structural geometry and deformation by exchanging the stiffness components, i.e., the structural elastic stiffness and geometrical stiffness. Based on the eigen-decomposition of the tangent stiffness matrix, the stiffness resistance to the deformation generated by a dominant load is quantified for any direction of eigenvector. The key structural stiffness is therefore defined and characterized by those eigenvalues and their corresponding eigenvectors with significant stiffness resistances. The contributions to the key structural stiffness are evaluated for the structural elastic stiffness and geometrical stiffness, respectively, and whether the decrease in key structural stiffness due to the pretension reduction can be compensated with the elastic stiffness by changing the cross-sectional areas of cables is analyzed. Then, the variations in isolated or closely spaced eigenvalues and their corresponding eigenvectors are estimated based on the first-order perturbation analysis of the tangent stiffness matrix. The underdetermined system of linear equations between the adjustments of the cross-sectional areas of cables and the expected variation in the key structural stiffness is established, and its least squares solution is employed to minimize the rehabilitation cost of the key structural stiffness. The proposed numerical strategy is applied to rehabilitate the key structural stiffness of an illustrative saddle-shaped cable net structure, whose pretension is proportionally decreased to different levels, by adjusting the cross-sectional areas of cables, and its accuracy and validity are verified. The applicability of the numerical strategy is also discussed in terms of the contribution coefficient of elastic stiffness to the key structural stiffness and the magnitude of pretension reduction.