共旋坐标系下考虑剪切变形的薄壁钢构件纤维梁单元

Fiber beam element for thin-walled stel members considering shear deformation based on co-rotational coordinate system

为实现复杂薄壁截面钢结构的静力弹塑性高效计算分析,提出一种共旋坐标系下考虑剪切变形的薄壁钢构件纤维梁单元。以中长薄壁构件为研究对象,梁单元的刚度矩阵基于欧拉梁理论推导而得。在该单元中,采用一维薄壁单元模拟薄壁截面,可以提供截面纤维信息,考虑材料非线性的影响,并可计算剪切系数,考虑剪切变形的影响。在求解过程中,使用共旋坐标系法扣除单元节点增量位移的刚体位移部分,以加快收敛速度。同时,还提出了材料非线性的数值调整策略,以提高单轴本构模型应用于考虑剪切变形梁单元中的适用性,并开发了专用的计算程序。对弯梁、坦拱、悬臂梁与柱的算例分析验证了所开发程序应对薄壁构件几何非线性、材料非线性计算的准确性;对带肋薄壁钢构件框架的计算分析则表明,该程序可有效预测复杂薄壁截面结构考虑剪切变形后的非线性响应。

To perform a static elastic-plastic analysis of complicated thin-walled box section steel structures with highly computational efficiency,a co-rotational coordinate system-based fiber beam element considering shear deformation for thin-walled steel members is proposed.Aiming at the intermediate-length members,the element stiffness matrix is derived based on the Euler beam theory.Thin-walled elements are adopted to simulate the thin-walled section,which can provide section fiber information for the consideration of material nonlinearity.And the section method can be adopted to calculate the shear deformation coefficients to consider the effect of shear deformation.In the solving process,rigid body displacements are eliminated by the co-rotational coordinate system method to expedite convergence.Meanwhile,a numerical adjustment strategy for material nonlinearity is presented,which can enhance the applicability of uniaxial constitutive model when it is applied to the beam element considering shear deformation.And corresponding calculation code is written.The analysis of curve beam,flat arch,cantilever beam and column verifies the accuracy of the developed program in handling geometric and material nonlinearity calculations of thin-walled components.Furthermore,calculations of frames with stiffened section steel members indicate that the developed program can effectively predict the nonlinear response of structures with complex thin-walled sections considering shear deformation.