Design sensitivity analysis for optimal design of geometrically nonlinear lattice structures

Abstract

Lattice structures are quite sensitive to the lateral wind loading and prone to the nonlinear behavior and lateral buckling. However, research on the design sensitivity analysis for lattice structures accounting for the geometric nonlinearity is rarely reported in the literature. An approach is proposed in this paper for the design sensitivity analysis for the nodal displacements, element stresses and critical load factor of linear and nonlinear lattice structures. For this, a design sensitivity formula of the global internal force vector with respect to design variables is first derived. A three-bar planar truss is then used to verify the proposed sensitivity analysis formula for the global internal force and the corresponding displacements and stresses. The ability of the proposed approach in estimating the critical load factor and computing its design sensibility is also proposed and compared with those results reported in the literature for a 3D roof structure. Good agreements between the results of the proposed approach with theoretical counterparts and those reported in the literature demonstrate that the proposed approach is effective and accurate. Finally, a real 3D lattice structure is adopted to investigate the application and effectiveness of the proposed approach for the design sensitivity analysis on the structure under wind actions. Results of design sensitivity for the lattice structure under wind actions show that the proposed approach could be used to estimate the design sensitivities effectively for both linear and nonlinear structural systems.