采用粘弹性人工边界时显式算法稳定性的改善研究

STABILITY IMPROVEMENT OF EXPLICIT ALGORITHM WHENUSING VISCOELASTIC ARTIFICIAL BOUNDARY

在显式动力计算中引入粘弹性人工边界时,受人工边界刚度和阻尼等因素影响,整体模型的数值积分稳定性将变得更为严格,这在一定程度上限制了粘弹性人工边界在大规模显式动力计算中的应用。该文基于对采用粘弹性人工边界的显式时域逐步积分算法稳定性条件的分析及其影响因素的研究,提出通过对人工边界附加集中质量来改善其数值积分稳定性的方法,发展了稳定性更优的改进粘弹性人工边界。为确定合理的人工边界质量值,利用基于局部子系统的稳定性分析方法推导得到改进粘弹性人工边界的稳定性条件,通过比较分析给出人工边界质量参数的建议值。采用该建议值后,粘弹性人工边界区的数值积分稳定性条件优于内部计算域的稳定性条件,整体计算模型的稳定性由内部计算域控制,此时可以用常规的稳定性判别准则来确定临界时间积分步长。数值算例表明,该文提出的粘弹性人工边界数值积分稳定性改善方法在提高计算效率的同时保持原人工边界的计算精度,具有较强的实用性。

When the viscoelastic artificial boundary is applied to explicit dynamic calculation,the stability conditions of the boundary area are more stringent than that of internal domain due to the stiffness and damping of artificial boundary,which limits the application of viscoelastic artificial boundary in large-scale explicit dynamic analysis.Based on the analysis of stability conditions and influencing factors of the viscoelastic artificial boundary in explicit time-domain stepwise integration algorithm,this study proposes a method to improve the numerical integration stability by introducing the lumped mass to the artificial boundary and thus develops an improved viscoelastic artificial boundary.In order to obtain the reasonable mass value of artificial boundary,the stability analysis method based on local boundary subsystem is used to derive the stability conditions of the improved viscoelastic artificial boundary,and then the recommended value of the lumped mass is obtained through comparative analysis.After adopting this recommended value,the stability condition of the artificial boundary area is looser than that of the internal calculation domain.Thus the overall numerical model is controlled by the internal domain.Then the conventional stability discrimination method can be used to estimate the critical integration time step that satisfies the stability condition.Numerical examples show that the method for improving the stability of viscoelastic artificial boundary proposed in this study can increase the calculation efficiency without losing the calculation accuracy.Therefore,it has strong practicability.