一种考虑杆件初始弯曲的非线性杆单元

Nonlinear link element considering member initial curvature

在假定杆件初始弯曲为半波正弦曲线的基础上,提出考虑初始弯曲的非线性杆单元,推导了轴力与轴向变形的关系和轴向切线刚度的表达式,得到了初始弯曲对轴向刚度的影响系数.分析表明,初始弯曲影响与刚度比、初始弯曲幅值、轴力大小以及杆单元长度有关.结合某索拱结构工程实例,研究不同初始预应力取值下,杆件初始弯曲对结构非线性稳定性能的影响程度和影响规律,结果表明:杆件初始弯曲对结构屈曲前的整体刚度影响很小,但对结构的极限荷载与屈曲后性能影响较大;初始预应力取值的增加对结构的位移控制非常有效,但是对结构的刚度影响却很小;在不同初始预应力取值下,极限荷载随杆件初始弯曲变化的规律相似,并且都接近于线性.非线性杆单元能够广泛应用于桁架结构和网格结构的设计与分析,在考虑杆件初始弯曲后,将使结构的设计与分析更加合理、更加科学.

Based on the assumption that the member initial curvature is half-wave sinusoid, a nonlinear link element considering the member initial curvature is brought forward. The relation between the member axial force and displacement is derived. The formulation of member axial tangent stiffness is obtained. And the influence of member initial curvature on axial tangent stiffness is also formulated. Results show that the influence of member initial curvature relates to the stiffness ratio, the value of initial curvature, the value of axial force and member element length. Pointing to a plane cable-arch structure, the influence of initial curvature on the structural nonlinear stability performance is investigated under different initial prestressing values. Results show that the initial curvature has little influence on the structural stiffness before buckling, while its influence on the structural beating capacity and post-buckling performance is remarkable. When the initial prestressing value varies, the relations between structural bearing capacity and member initial curvature are similar and nearly linear. The proposed nonlinear link element can be applied extensively to the design and analysis of plane truss and spatial reticulated structures. When the member initial curvature is considered, the design and analysis can be more reasonable.