A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deforme...A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2^＊ derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2^＊ and C2. A stiffness matrix is obtained in C2^＊; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2^＊ is transformed into that in CI. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.展开更多
以三维连续体的虚功增量方程为基础,采用平动和转角位移分别插值的方法,导出了三维空间梁结构大位移、大转动问题内力分析的 UL 法(Updated Lagrangian FormuIation)。考虑轴向、剪切、弯曲和扭转效应,提出了新的几何刚度矩阵,并建立了...以三维连续体的虚功增量方程为基础,采用平动和转角位移分别插值的方法,导出了三维空间梁结构大位移、大转动问题内力分析的 UL 法(Updated Lagrangian FormuIation)。考虑轴向、剪切、弯曲和扭转效应,提出了新的几何刚度矩阵,并建立了描述大转动规律的坐标转换矩阵。算例表明,依本文方法编制的程序具有分析结构强几何非线性行为的能力;在满足本文假定(即每次加载增量中转角增量是小量)的条件下,可以描述任意大角度的刚体转动。展开更多
文摘A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2^＊ derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2^＊ and C2. A stiffness matrix is obtained in C2^＊; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2^＊ is transformed into that in CI. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.
文摘以三维连续体的虚功增量方程为基础,采用平动和转角位移分别插值的方法,导出了三维空间梁结构大位移、大转动问题内力分析的 UL 法(Updated Lagrangian FormuIation)。考虑轴向、剪切、弯曲和扭转效应,提出了新的几何刚度矩阵,并建立了描述大转动规律的坐标转换矩阵。算例表明,依本文方法编制的程序具有分析结构强几何非线性行为的能力;在满足本文假定(即每次加载增量中转角增量是小量)的条件下,可以描述任意大角度的刚体转动。
