爆炸荷载下混凝土构件动力方程的差分解

Solution to the dynamical equations of reinforced concrete elements under blast loads with the finite difference method

爆炸荷载下混凝土构件的动力方程为非齐次偏微分方程,通常采用数值法迭代求解,迭代过程需同时考虑材料非线性和应变率效应。采用差分法求解爆炸荷载下构件的动力方程,同时考虑弯曲变形和剪切变形,将材料非线性和应变率效应融入差分迭代过程,应用分层法模型计算节点弯矩,考虑混凝土开裂引起的截面弯曲刚度退化和变形的非线性变化,这些改进步骤,提高了分析的严密性和精确度。差分结果与他人实验数据吻合良好,与LS-DYNA有限元分析具有相当的精度。

The dynamical equations of the reinforced concrete under blast loads were the non-homogeneous partial differential equations,it was usually investigated numerically by an iterative method,in the meantime,the nonlinear of material behavior and the strain rate effect should be taken into account in the iterative process.A finite difference method was used to solve numerically the dynamical equations of structural concrete elements under blast loads,it can simultaneously accommodate flexural and shear deformations,incorporated the nonlinear of material behavior and the strain rate effects on the strength of the concrete and steel into the each step of the iterative process,utilized the layered analysis model to compute the node moments,took over the nonlinear degradation of cross-sectional flexural rigid and the nonlinear variation of deformation caused by concrete crack.These improved procedures up-graded the tightness and accuracy of the numerical investigation.The results from the finite difference method agreed well with the experimental data obtained by other investigators,and had the same accuracy with the results by applying the LS-DYNA.