| 方德平.修正荷载的Wilson-θ法的稳定性与精度分析[J].计算力学学报,2012,29(2):195~199 |
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| 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 |
| 投稿时间：2010-10-16 修订日期：2011-05-18 |
| DOI：10.7511/jslx20122008 |
| 中文关键词: Wilson-θ法 稳定性 计算精度 荷载修正 谱半径 |
| 英文关键词:Wilson-θ method stability calculation accuracy load modification spectral radius |
| 基金项目: |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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