基于拟力法的纤维梁有限元非线性分析方法

Nonlinear fiber beam element analysis based on force analogy method

以拟力法中的弹塑性分解思路和纤维梁理论为基础,将梁单元的截面变形分解为弹性变形和塑性变形,并引入塑性自由度,在材料层面建立了基于拟力法的纤维梁有限元非线性分析方法。该方法可以保持结构整体刚度矩阵不变,其非线性状态通过局部塑性矩阵加以体现,在迭代计算时避免了结构整体刚度矩阵的实时更新与分解,且塑性矩阵相比于结构整体刚度矩阵规模小,提高了计算效率。通过数值算例,将文中方法与采用有限元软件ABAQUS的分析结果进行对比,两者吻合较好,证明了该方法的有效性。

Based on the basic idea of deformation decomposition in the force analogy method （ FAM ）, the section deformation is decomposed into elastic and plastic components and the plastic degrees of freedom are introduced. A nonlinear fiber beam element analysis method for building structures is presented through incorporating the FAM into the framework of fiber beam element. The initial stiffness matrix is used and the inelastic behavior of structure can be calculated by using the plastic stiffness matrix. The efficiency of nonlinear analysis is improved due to relatively small plastic stiffness matrix iteration such that the updating and factorization of tangent stiffness matrix of the classical finite element formulation are avoided during iteration process. The numerical results show that the presented method agrees well with the results by software ABAQUS, which verifies the effectiveness of proposed method.