空间梁单元切线刚度矩阵的精确分析方法

Accurate Analysis Method on Tangent Stiffness Matrix for Space Beam Element

为有效进行空间刚架结构后屈曲分析,提出一种新的空间梁单元切线刚度矩阵的精确分析方法。首先用直接法建立梁单元杆端力与杆端位移的增量关系式,然后根据矩阵微分理论求出单元杆端力关于杆端位移的导数,在求导结果表达式中令杆端位移增量为0,即可得到梁单元切线刚度矩阵。对六层和二十层空间刚架结构进行了后屈曲分析。结果表明:所得的空间梁单元切线刚度矩阵具有足够精度,可有效用于大型空间刚架结构的后屈曲分析。

In order to effectively conduct the post‐buckling analysis for space frame , a new accurate analysis method for the tangent stiffness matrix of space beam element was proposed . Firstly ,the incremental force and displacement of the member ends for space beam element was established using direct equilibrium method ,and then derivation of the member‐end force was determined with regard to the member‐end displacement according to the matrix differentiation theory and the increment of member‐end displacement of the derivation expression was set equal to zero ,so that the tangent stiffness matrix for space beam element was obtained .The post‐buckling analyses for a six‐storey space frame and a twenty‐storey frame were done .The results show that the present tangent stiffness matrix for space beam element has enough precision ,and can be applied to the post‐buckling analysis for large space frame .