基于有限单元柔度法的材料与几何双重非线性空间梁柱单元

Material and geometrically nonlinear spatial beam-column element based on the finite element flexibility method

从有限单元柔度法的基本思想出发,基于完全拉格朗日格式(TL格式),建立了能考虑材料与几何双重非线性的一般化空间梁柱单元,适用于满足Euler-Bernoulli梁柱二阶分析理论假定的空间杆系结构非线性分析。另外,在梁柱单元截面分析中引入纤维模型,使其适用于解决钢筋混凝土这类复合材料结构的非线性分析问题。对钢筋混凝土双向偏心受压柱试验结果的模拟分析表明,本文所提方法是正确、可靠的,能有效地分析钢筋混凝土框架柱的材料与几何双重非线性问题。

Based on the basic idea of the finite element flexibility method and total Lagrangian formulation （TL formulation）, the general spatial beam-column element with dual nonlinearity of material and geometry is established in this paper. The proposed beam-column element is applicable to the general nonlinear analysis of spatial framed structures that satisfy the basic assumptions of the second-order theory for Euler-Bernoulli beam-columns. Moreover, Fiber-model is introduced into the sectional analysis of the proposed beam-column element so that it can be applied to the nonlinear analysis of composite material structures such as reinforced concrete. Numerical simulations of experiment on reinforced concrete two-way eccentrically loaded columns shows that the proposed formulation is correct and reliable, and can effectively solve the dual nonlinear problem of material and geometry for reinforced concrete frame columns.