双尺度一致割线刚度算子的第二类BFGS表达方法

BFGS UPDATE METHOD OF SECOND KIND FOR TWO-LEVEL CONSISTENT SECANT OPERATORS

将双尺度一致割线刚度算子的第二类BFGS表达方法纳入到混凝土双标量弹塑性损伤本构模型。为了在计算效率和稳健性之间寻求一个较好的平衡点,在结构尺度,采用拟牛顿方法进行刚度矩阵更新求解;在材料尺度,通过第二类BFGS更新方法构造刚度矩阵进行迭代求解。基于第一类和第二类BFGS更新算式,建立了一维和二维的混凝土弹塑性损伤本构,采用两尺度一致割线刚度的求解策略,对钢筋混凝土柱和剪力墙在反复荷载作用下的滞回行为进行了分析。结果表明:两类BFGS割线刚度算子的构造方法对梁柱单元的分析均具有较好的适用性。而墙板分层壳单元的分析结果表明:第二类BFGS表达方法较第一类BFGS表达方法具有更好的数值稳定性。

The BFGS update method of second kind for two-level consistent secant operators is incorporated into the double scalar damage plasticity model.In order to make a good trade-off between computational efficiency and robustness,the quasi-Newton method is adopted to update the stiffness matrix and solve the equilibrium equation at structural level,and the BFGS update method of second kind is adopted to update the stiffness matrix for nonlinear material model.The one dimensional and two dimensional constitutive relationships of concrete are established based on the first and second kind of BFGS update method,and the two-level solution strategy is adopted to analyze the hysteretic behavior of reinforced concrete column and shear wall.The results reveal that both update methods are applicable to the beam element analysis,whereas the results of layered shell element analysis indicate that the BFGS update method of second kind has better numerical stability than that of first kind.