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提出了一种几何非线性有限元分析平面框架的方法。应用修正拉格朗日(UL)法计算单元的增量节点位移;计算增量节点力采用了协同转动法,使用的协同构形(Cr)是由前一个平衡构形(C1)经刚体运动后得到。以单元节点的增量自然变形为参数表示出Cr构形下的虚功方程;推导得出了C1构形中单元增量节点位移向量与Cr构形中节点增量自然变形之间的关系;把得到的关系式代入虚功方程,得Cr构形中计算增量节点力的切向刚度矩阵;所得的切线刚度矩阵能通过刚体检验。考虑了加载变形对后续分析的影响,导致切向刚度矩阵增加了与加载变形有关的刚度矩阵。算例结果表明:提出的方法可以采用较少单元达到UL法同样的计算精度;加载变形产生的刚度矩阵能有效地提高计算效率;但变形较大时,加载变形产生的刚度矩阵会导致膜锁。
A method of geometric nonlinear finite element analysis of planar frame is proposed. The modified Lagrangian (UL) method is used to calculate the displacement of incremental nodes. The incremental nodal force is calculated by the method of coordinated rotation. The coordinated configuration (Cr) used by the previous equilibrium configuration (C1) After getting. The virtual work function in Cr configuration is represented by incremental natural deformation of element node. The relationship between displacement vector of element incremental node in C1 configuration and natural deformation of node in Cr configuration is deduced. The relation obtained is substituted into the virtual work equation to obtain the tangential stiffness matrix for calculating the incremental nodal forces in the Cr configuration; the resulting tangent stiffness matrix can pass the rigid body test. The effect of loading deformation on subsequent analysis is considered, resulting in an increase of the stiffness matrix associated with loading deformation in the tangential stiffness matrix. The experimental results show that the proposed method can achieve the same calculation accuracy with less units by using fewer elements. The stiffness matrix generated by loading deformation can effectively improve the computational efficiency. However, when the deformation is large, the stiffness matrix generated by loading deformation can lead to membrane lock .