考虑非黏性阻尼的黏弹性DDA解法

发布时间：2018-03-28 04:07

本文选题：数值分析　切入点：非黏性阻尼　出处：《岩石力学与工程学报》2017年S2期

【摘要】：将非黏性阻尼引入到DDA方法中,用以分析非黏性阻尼对于非连续黏弹性结构的影响。首先,将非黏性阻尼引入到块体系统的运动方程中,发现微分形式运动方程难以求解的问题。其次,通过黏弹性结构的力与位移的关系以及Newmark积分方案,推导得到具有对称系数矩阵的含有非黏性阻尼的等价DDA运动方程。最后,结合具体算例,分别分析在恒力作用下和谐振激励作用下的块体位移响应,通过比较DDA计算值和理论值,验证提出的含有非黏性阻尼的黏弹性结构DDA解法的正确性。研究结果表明该考虑非黏性阻尼的DDA方法是一种高效的处理黏弹性问题的解法,这为分析黏弹性结构的非连续变形提供了新思路。
[Abstract]:The non-viscous damping is introduced into the DDA method to analyze the influence of the non-viscous damping on the discontinuous viscoelastic structure. Firstly, the non-viscous damping is introduced into the motion equation of the block system. It is found that differential equations of motion are difficult to solve. Secondly, through the relationship between force and displacement of viscoelastic structures and Newmark integral scheme, an equivalent DDA equation of motion with non-viscous damping with symmetric coefficient matrix is derived. Combined with concrete examples, the displacement responses of blocks under constant force and resonant excitation are analyzed, and the calculated and theoretical values of DDA are compared. The validity of the proposed DDA solution for viscoelastic structures with non-viscous damping is verified. The results show that the DDA method with non-viscous damping is an efficient solution for viscoelastic problems. This provides a new idea for analyzing the discontinuous deformation of viscoelastic structures.
【作者单位】：武汉大学水资源与水电工程科学国家重点实验室;长江勘测规划设计研究有限责任公司;
【基金】：国家重点基础研究计划(973)项目(2015CB057904) 国家自然科学基金面上项目(51579191)~~
【分类号】：TU45

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