初始荷载影响下梁静力特性的有限元分析

Based on nonlinear elastic theory and Hamilton's principle, a finite element formula is derived to analyze the static characteristics of beams under the effect of flexural and axial stresses induced by initial load and a generalized element stiffness matrix, which incorporates the effect of initial flexural stress as well as geometric stiffness, is presented. The finite element formula is verified through a comparison in results with the analytical solution. The effects of key physical factors including the type and magnitude of initial load, and stiffness parameters such as sectional inertia moment, inertia radius and span, on the static characteristics of the beams with various restraint conditions are discussed, with the effect of initial flexural stress considered. The results show that with the initial in existence, the static characteristics induced by later-applied loads would become reduced and extent of this reduction relates to the magnitude of initial load, stiffness and restraining conditions of the beam. Some suggestions for the design of lightweight structures are given.