修正荷载的Wilson-θ法的稳定性与精度分析  

Stability and accuracy of Wilson-θ method with load modification

作　　者：方德平[1] 

机构地区：[1]华侨大学土木工程学院,泉州362021

出　　处：《计算力学学报》2012年第2期195-199,共5页Chinese Journal of Computational Mechanics

摘　　要：Wilson-θ法求得的位移、速度与加速度不满足t时刻的动力平衡方程。提出修正荷载的Wilson-θ法:增加一个荷载δF(t),使得t时刻的动力平衡方程得以满足;将-θ′δF(t)作为荷载加入t+Δt时刻的计算中,当θ′=0时,修正荷载的Wilson-θ法退化为Wilson-θ法。对应于不同的θ′值,在无条件稳定的前提下,θ的取值范围也不同。定义了逐步积分法中的计算误差。计算结果表明:计算误差与θ值成正相关,当θ′=0.6,无条件稳定的θ为最小值1.24,因而θ′=0.6,θ=1.24时,计算误差最小,建议在计算中采用。保持Wilson-θ法无条件稳定、几乎不增加计算量的条件下,修正荷载的Wilson-θ法可以提高计算精度。The displacement,velocity and acceleration obtained by Wilson-θ method don＇t meet the dynamic equilibrium equations at the time t.Wilson-θ method with load modification is put forward,that is,a load δF（t） is added to meet the dynamic equilibrium equations at the time t,then the load modification-θ′δF（t） is added into calculation as load at the time t＋Δt,when θ′=0,Wilson-θ method with load modification returns to Wilson-θ method.On condition of unconditional stability,the range of θ value is different for different values of θ′.The calculation error is defined in time-stepping method,the calculation results indicate：positive correlation exists between the calculation error and θ value;for θ′=0.6,θ value with unconditional stability is minimum 1.24,therefore,the calculation error for θ′=0.6,θ=1.24 is minimum,which is suggested to be used in calculation.Maintaining the unconditional stability,almost not increasing the calculation quantity,Wilson-θ method with load modification can improve the calculation accuracy.

关 键 词：WILSON-Θ法 稳定性 计算精度 荷载修正 谱半径 

分 类 号：O317[理学—一般力学与力学基础]