复合隐式时间积分格式的非线性问题仿真研究

Simulation Study on Nonlinear Problems Using Composite Implicit Time Integration Procedure

梯形时间格式在求解某些非线性问题时会出现失稳现象,无法获得收敛解,为了验证复合隐式时间积分格式在求解此类非线性问题时的优越性,通过比较分析数值耗散的大小确定复合隐式时间积分格式中γ的合理取值。通过Updated La-grangian方法建立非线性运动增量方程,应用9节点四边形单元划分计算域网格。分析比较了相同时间步长,γ取值对研究对象的位移、速度和加速度时程曲线的影响。悬臂梁承受恒定集中力和承受冲击载荷的算例均表明:γ取0.2时复合隐式积分格式引入的数值耗散较小,精度较高。

When solving some nonlinear problems using trapezoidal rule, the numerical results may become insta- ble and could not converge. In this paper, the composite implicit time integration procedure was implemented in non- linear dynamic problems in order to verify its superiority and to determine a proper γaccording to numerical dissipa- tion. The updated Lagrangian method was employed to develop the nonlinear incremental equations. 9-node quadri- lateral elements were implemented to mesh the computational domain. The different performances on displacement, velocity and acceleration time-history curves were compared at different γ with the same time step. The cantilever problems under both constant and instant loads show ： when γis 0.2, the numerical results have smaller dissipation and higher precision.