CAJ | 학술논문

基于Hellinger-Reissner变分建立了一种用于几何和材料非线性分析的混合单元，采用位移形函数和考虑二阶效应的内力形函数对截面位移和截面内力进行插值，建立混合控制微分方程；通过静力凝聚消除单元节点力未知量得到单元刚度矩阵和单元内力。单元状态确定过程中，截面层次的平衡方程和单元层次的协调方程均通过引入非线性迭代算法以消除残余误差，从而减少结构层次的迭代次数。混合单元结合纤维截面模型用于钢管混凝土(CFST)构件的数值分析，结果表明：相对于刚度法和柔度法单元，基于 Hellinger-Reissner 变分的混合单元可以更加准确地反映构件的几何和材料非线性，非线性迭代算法用于单元状态确定具有良好的计算效率和数值稳定性。在此基础上对影响CFST构件几何非线性的主要参数进行了分析。
기우Hellinger-Reissner변분건립료일충용우궤하화재료비선성분석적혼합단원，채용위이형함수화고필이계효응적내력형함수대절면위이화절면내력진행삽치，건립혼합공제미분방정；통과정력응취소제단원절점력미지량득도단원강도구진화단원내력。단원상태학정과정중，절면층차적평형방정화단원층차적협조방정균통과인입비선성질대산법이소제잔여오차，종이감소결구층차적질대차수。혼합단원결합섬유절면모형용우강관혼응토(CFST)구건적수치분석，결과표명：상대우강도법화유도법단원，기우 Hellinger-Reissner 변분적혼합단원가이경가준학지반영구건적궤하화재료비선성，비선성질대산법용우단원상태학정구유량호적계산효솔화수치은정성。재차기출상대영향CFST구건궤하비선성적주요삼수진행료분석。
This paper proposed a beam-column mixed element based on Hellinger-Reissner variation for geometric and material nonlinear analysis. A governing differential formulation of mixed element is established using displace-ment shape function and force shape function including second-order effects for interpolation of section deformation and innerforce,respectively.The element stiffness matrix and internal forces are derived by eliminating the force unknown through static condensation. During the element state determination,nonlinear iteration algorithm is adopted for residual error of section equilibrium and element compatibility,which reduces the numerical cost of structural equilibrium iteration. This mixed element based fiber section is used for numerical studies of concrete filled steel tube(CFST) members,and the results indicate good agreement. Relative to the displacement-based and flexibil-ity-based elements,the mixed element based Hellinger-Reissner variation was more reasonable in predicting geomet-ric and material nonlinearity of members,and the nonlinear iteration algorithm carried out for element state determi-nation is of good efficiency and stability. Finally,a parametric study for geometric nonlinearity of CFST was per-formed based on the mixed element model.