基于稳定函数的空间薄壁构件几何刚度矩阵

为真实描述结构二阶弹性分析中可能出现的侧扭屈曲变形和翘曲扭转变形,精确满足增量虚位移原理,结合梁柱法和有限单元法,基于更新拉格朗日构形的增量虚位移原理和三维空间薄壁构件理论,提出采用拉弯、压弯、纯弯及扭转状态下薄壁构件平衡微分方程的解作为插值函数,详细推导了考虑截面翘曲影响的空间薄壁梁柱单元的几何非线性切线刚度矩阵,推导过程中同时考虑了双向弯曲和扭转及其各耦合项对刚度矩阵的影响。并通过算例证实了文中方法的精确度和有效性。

Geometric Stiffness Matrix of Space Thin walled Member Based on Stability Functions

In order to correctly describe the lateral-torsion buckling and warping deformations,and to satisfy the incremental virtual displacement principle,the solution of equilibrium differential equations under stretch-bending,compression-bending,pure bending and torsion is taken to be the interpolation function,and the geometrical nonlinear stiffness matrix of the space thin-walled beam-column element considering the cross-section warping effect is derived in detail,according to the increment virtual displacement principle based on the updated Lagrange configuration and 3D space thin-walled member theory,the stiffness matrix can be used to deal with the dual-flexure,torsion and their coupling effects.The accuracy and efficiency of the proposed analytical method are verified by numerical examples.