粘弹性人工边界在ABAQUS中的实现及应用
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摘要
基于柱面波理论的二维时域人工边界,建立了人工边界点相对于散射波源的局部坐标系下的等效物理系统,利用人工边界点局部坐标系与整体坐标系的转换矩阵,推导了整体坐标下人工边界的等效物理参数,并考虑边界点与散射波源的距离变化,利用该等效物理系统模拟人工边界的散射效应,二维均匀半空间算例验证该法可减弱边界几何形状的影响,且具有较好的精度和适用性。应用该法探讨了不同地基刚度对重力坝非线性开裂损伤的影响,结果表明,地基弹性模量越小,人工边界散射的能量越多,开裂损伤的范围就越小。
Based on two dimensional time-domain artificial boundary with cylindrical wave theory,equivalent physical system is established in local coordinate system,which artificial boundary points is relative to the scattered wave sources.With the transformation matrix between global and local coordinate system at artificial boundary point,equivalent physical parameters of the artificial boundary in global coordinate system are deduced.The system is used to simulate scattering effect of artificial boundary by considering the distance change between boundary points and scattered wave sources.The 2D uniform half-space example demonstrates that the proposed method can reduce the influence of geometry shape boundary,which has good precision and applicability.The influence of different foundation stiffness on non-linear crack damage of gravity dam is studied by the proposed method.The results show that lower elastic modulus of foundation will lead to more dispersed energy for artificial boundary and lesser crack damaged area.
Based on two dimensional time-domain artificial boundary with cylindrical wave theory,equivalent physical system is established in local coordinate system,which artificial boundary points is relative to the scattered wave sources.With the transformation matrix between global and local coordinate system at artificial boundary point,equivalent physical parameters of the artificial boundary in global coordinate system are deduced.The system is used to simulate scattering effect of artificial boundary by considering the distance change between boundary points and scattered wave sources.The 2D uniform half-space example demonstrates that the proposed method can reduce the influence of geometry shape boundary,which has good precision and applicability.The influence of different foundation stiffness on non-linear crack damage of gravity dam is studied by the proposed method.The results show that lower elastic modulus of foundation will lead to more dispersed energy for artificial boundary and lesser crack damaged area.
引文
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[5]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1 070-1 075.
[6]刘晶波,谷音,李彬.结构地基开放系统动力相互作用问题的高效解法[J].土木工程学报,2006,39(5):112-121.
[7]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.
[8]李静,陈健云.动力相互作用分析中无质量地基的应用研究[J].世界地震工程,2007,23(2):58-62.
[2]Medina F,Tailao R.Finite Element Technicals forProblems of Unbounded Domains[J].InternationalJoumal for Numerical Methods in Engineering,1983,19(4):1 209-1 226.
[3]Lysmer J,Kuhlemeyer R L.Finite Dynamic Modelfor Infinite Media[J].Journal of the EngineeringMechanics Division(EM4),1969,95:859-877.
[4]Deeks A J,Randolph M F.Axisymmetric Time-do-main Transmitting Boundary[J].Journal of Engi-neering Mechanics,1994,120(1):25-42.
[5]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1 070-1 075.
[6]刘晶波,谷音,李彬.结构地基开放系统动力相互作用问题的高效解法[J].土木工程学报,2006,39(5):112-121.
[7]杜修力,赵密,王进廷.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.
[8]李静,陈健云.动力相互作用分析中无质量地基的应用研究[J].世界地震工程,2007,23(2):58-62.
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