摘要
分析梁单元修正拉格朗日法的刚体检验和增量节点力计算.根据欧拉-伯努利假定,推导考虑2阶效应的截面转角表达式,得出转角不仅与横向位移导数有关,还与轴向位移导数有关.采用虚功原理,推导出符合刚体检验的几何刚度矩阵,指出几何刚度矩阵不满足刚体检验的原因是采用了转角与横向位移导数的线性假定.分析多种计算增量节点力的方法;利用同一刚度矩阵计算增量节点位移、增量节点力,得出欲求构形的节点力向量后,必须通过由已知构形到欲求构形的近似坐标变换得到欲求构形单元的轴力、剪力、弯矩和扭矩.数值计算结果表明,采用切线刚度矩阵计算增量节点力的方法是有效的,几何刚度矩阵通过刚体检验与否对计算结果无明显影响.
The rigid body test and the recovery of incremental nodal forces were analyzed for an updated Lagrangian formulation of beam element. The expressions of cross-sectional rotation considering the second order effects were formulated based on the Euler-Bernoulli hypothesis. Results showed that a crosssectional rotation was related to the derivative of axial displacement and the derivative of transversal displacement. A geometric stiffness matrix which passed a rigid body test was derived by using the principle of virtual work. The reason for some geometric stiffness matrix does not pass a rigid body is the adoption of a linear relation between the cross-sectional rotation and the derivative of transversal displacement. Several methods for recovery of the nodal forces were analyzed. For the method with the same stiffness matrix to calculate incremental nodal displacements and incremental nodal forces, it is essential to transform previous nodal forces into axial forces, shear forces, bending moments and torques in the desired configuration by an approximate coordinate transformation between the unknown configuration and the desired configuration after the nodal forces were obtained for a desired configuration. The numerical examples demonstrate that it is effective to recover the incremental nodal forces with a tangent stiffness matrix, and a geometric stiffness matrix passing a rigid body test or not has no significant influence on the numerical results.
出处
《浙江大学学报（工学版）》
EI
CAS
CSCD
北大核心
2010年第10期1992-1997,2028,共7页
Journal of Zhejiang University：Engineering Science
关键词
非线性有限元法
修正的拉格朗日法
梁单元
几何刚度矩阵
刚体检验
nonlinear finite element method
updated Lagrangian formulation
beam element
geometric stiffness matrix
rigid body test
