Geometric nonlinear analysis based on the generalized displacement control method and orthogonal iteration - Li Ling (Nonlinear Engineering)
In response to the shortcomings of insufficient efficiency in calculating geometric nonlinear features and high environmental impact in the current construction, this study explores the control of nonlinear geometric structures based on an updated Lagrangian model function in the construction. In this method, the change in the geometric nonlinear stiffness is analyzed using generalized stiffness parameters and a displacement increment method, and the iteration step size and loading/unloading directions are adjusted in the iteration process to achieve the convergence of the solution. In the simulation experiment, the proposed method took 126 s to calculate the incremental iteration steps 700 times in a conventional environment, which is 28.8% more efficient than the cross-sectional method. In the simulated disaster environment, the model took 1,615 s to calculate the ultimate load of 84 contact elements, which is 43.1% more efficient than the section method and 62.6% more efficient than the discrete analysis method. Experimental results showed that the displacement judgment calculation efficiency of the method proposed in this study is higher than that of other models under different loading and unloading conditions and even in geological disaster states. This method had high environmental adaptability in solving nonlinear building structures and could improve the efficiency of solving general nonlinear building results.