界面半圆形夹杂脱胶结构在瞬态SH波作用下的数值模拟
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摘要
本文采用有限元法研究近场界面圆柱形夹杂脱胶结构对瞬态SH波的散射和动应力集中系数问题。有限元法在数学上是将偏微分方程的初边值问题划归一组常微分方程的初值问题(在空间离散化之后)或一组规则代数方程。然后,用NEWMARK直接积分法进行求解,得到各节点和单元的位移、应力的时程解。用有限元法模拟弹性波在半无限介质中的传播问题,由于受计算机存储空间、计算速度的限制,需要用有界区域代替无界区域。其首要问题是人工边界的设置问题,由于要从无限域中截取有限区域来模拟无限域,所以要引入人工边界。其次是解决时空离散带来的各种不利影响,以减少误差。还要考虑荷载的施加问题以及模型大小对解题的影响问题。本文对要解决的问题建立了有限元模型,并用通用有限元分析软件ANSYS进行了计算,给出了部分节点的位移、应力时程解和夹杂周边的动应力集中系数,并对结果进行了讨论。本文的具体工作如下：
1、介绍波动数值模拟的基本概念、研究状况和基本方法以及在工程中的应用；阐述有限元的基本原理和波动有限元的基本求解方法；讨论应用波动有限元方法求解问题时可能产生的主要的误差并提出了具体的解决办法。
2、采用有限元法研究算例一：界面附近含有下半圆形脱胶的圆柱形弹性夹杂的散射和动应力集中问题。本文对所要解决的问题建立了有限元模型,并用通用有限元分析软件ANSYS进行了计算,给出了部分节点的时程解和动应力集中系数的数值结果,讨论圆柱形弹性夹杂、介质参数以及波数对动应力集中和各点位移的带来的不同影响,并进行对比分析。
3、采用有限元法研究算例二：界面附近含有上半圆形脱胶的圆柱形弹性夹杂的散射和动应力集中问题。和算例一类似,通过对比介质参数的变化来对比分析各点的位移和加速度以及夹杂周围的动应力集中系数。最后,通过两个上、下脱胶两个算例的对比来分析脱胶位置的不同对结构上各点位移、加速度和动应力集中系数带来的不同变化,并参照理论解,给出分析结果,为实际工程中的应用提供一定的依据。
This thesis investigates the scattering problem and the dynamic stress concentration coefficient problem of transient state SH-wave by an interface cylindrical inclusion with disconnected curve in near field by the method of FEM. The FEM is a method of which transforms the issue of partial differential-coefficient equation's initial and boundary value to the problem of ordinary differential-coeffeient equation's initial and boundary value (after space been dispersed) or a set of regular algebra equations. Then, use the direct integral calculus method of NEWMARK to get each node's and element's displacement and stress vs. time. As been limited by computer's memory capacity and computation speed, when simulating the transmition of elastic wave in semi-infinite medium by the method of FEM, needs to replace the unbounded area by bounded area. The first problem is the set of artificial boundary, because of the using of finite area, which replaces infinite area, to simulate infinite area. The next is to solve each disadvantage caused by space-time dispersing, in order to reduce error. In addition, the problems of inflicting load and model's size should be considered. In this article, we found the finite element model in allusion to the problems above, solve the equations by the general finite element analysis software ANSYS, get part of the nodes'displacement and stress solution vs. time and the dynamic stress concentration coefficient at the edge of cavity, and discuss the result. The main works are as follows:
1、The basic concept, current research status, basic method and the application in engineering of the numerical simulation of wave are introduced, the keystone of the FEM and the solving method of the wave, which the FEM are explained, the possible error growing out of the using of the wave FEM and the concrete measures are discussed.
2、The first analysis example solves the scattering and dynamic stress concentration problem of SH-wave by an interface cylindrical elastic inclusion with an under semicircular disconnected curve. The finite element model is founded and computed by the software ANSYS. Get the values of part of the nodes' displacement and stress solution vs. time and the dynamic stress concentration coefficient. Discuss the effect of cylindrical elastic inclusion, the parameter of medium and the wave on dynamic stress concentration and each node's displacement. The contrast is also put up.
3、The second analysis example solves the scattering and dynamic stress concentration problem of SH-wave by an interface cylindrical elastic inclusion with an upper semicircular disconnected curve. Similar to the first example, the contrast analysis of each node's displacement, acceleration and the dynamic stress concentration coefficient is discussed by the contrast of the change of medium's parameter. At last, the effect of different disconnected curve position on each node's displacement, acceleration and the dynamic stress concentration coefficient is analysed by the contrast of the two examples. The result is given by consulting the theoretical solution, which provides some references for the application on practical engineering.
1、介绍波动数值模拟的基本概念、研究状况和基本方法以及在工程中的应用；阐述有限元的基本原理和波动有限元的基本求解方法；讨论应用波动有限元方法求解问题时可能产生的主要的误差并提出了具体的解决办法。
2、采用有限元法研究算例一：界面附近含有下半圆形脱胶的圆柱形弹性夹杂的散射和动应力集中问题。本文对所要解决的问题建立了有限元模型,并用通用有限元分析软件ANSYS进行了计算,给出了部分节点的时程解和动应力集中系数的数值结果,讨论圆柱形弹性夹杂、介质参数以及波数对动应力集中和各点位移的带来的不同影响,并进行对比分析。
3、采用有限元法研究算例二：界面附近含有上半圆形脱胶的圆柱形弹性夹杂的散射和动应力集中问题。和算例一类似,通过对比介质参数的变化来对比分析各点的位移和加速度以及夹杂周围的动应力集中系数。最后,通过两个上、下脱胶两个算例的对比来分析脱胶位置的不同对结构上各点位移、加速度和动应力集中系数带来的不同变化,并参照理论解,给出分析结果,为实际工程中的应用提供一定的依据。
This thesis investigates the scattering problem and the dynamic stress concentration coefficient problem of transient state SH-wave by an interface cylindrical inclusion with disconnected curve in near field by the method of FEM. The FEM is a method of which transforms the issue of partial differential-coefficient equation's initial and boundary value to the problem of ordinary differential-coeffeient equation's initial and boundary value (after space been dispersed) or a set of regular algebra equations. Then, use the direct integral calculus method of NEWMARK to get each node's and element's displacement and stress vs. time. As been limited by computer's memory capacity and computation speed, when simulating the transmition of elastic wave in semi-infinite medium by the method of FEM, needs to replace the unbounded area by bounded area. The first problem is the set of artificial boundary, because of the using of finite area, which replaces infinite area, to simulate infinite area. The next is to solve each disadvantage caused by space-time dispersing, in order to reduce error. In addition, the problems of inflicting load and model's size should be considered. In this article, we found the finite element model in allusion to the problems above, solve the equations by the general finite element analysis software ANSYS, get part of the nodes'displacement and stress solution vs. time and the dynamic stress concentration coefficient at the edge of cavity, and discuss the result. The main works are as follows:
1、The basic concept, current research status, basic method and the application in engineering of the numerical simulation of wave are introduced, the keystone of the FEM and the solving method of the wave, which the FEM are explained, the possible error growing out of the using of the wave FEM and the concrete measures are discussed.
2、The first analysis example solves the scattering and dynamic stress concentration problem of SH-wave by an interface cylindrical elastic inclusion with an under semicircular disconnected curve. The finite element model is founded and computed by the software ANSYS. Get the values of part of the nodes' displacement and stress solution vs. time and the dynamic stress concentration coefficient. Discuss the effect of cylindrical elastic inclusion, the parameter of medium and the wave on dynamic stress concentration and each node's displacement. The contrast is also put up.
3、The second analysis example solves the scattering and dynamic stress concentration problem of SH-wave by an interface cylindrical elastic inclusion with an upper semicircular disconnected curve. Similar to the first example, the contrast analysis of each node's displacement, acceleration and the dynamic stress concentration coefficient is discussed by the contrast of the change of medium's parameter. At last, the effect of different disconnected curve position on each node's displacement, acceleration and the dynamic stress concentration coefficient is analysed by the contrast of the two examples. The result is given by consulting the theoretical solution, which provides some references for the application on practical engineering.
引文
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[2]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京：科学出版社,1993：72-202页
[3]蔡之瑞.1995年1月17日日本阪神地震——直下型冲击.世界地震工程.1995(1)：1-4
[4]钟伟芳,聂国华著.弹性波的散射理论.武汉：华中理工大学出版社,1997：137-189页
[5]王铎,马兴瑞,刘殿魁.弹性动力学最新进展.北京：科学出版社,1995：13-15页
[6]周锡元、高小旺等编著.抗震工程学.北京：中国建筑工业出版社,2000
[7]刘儒勋、王志峰.数值模拟方法.中国合肥,中国科技大学出版社,2001
[8]洪善桃.关于弹性波近代发展的概述.上海力学,1986(3)：66-77
[9]Kriegsmann G A, Norris A N, Reiss E L. Scattering by Penetrable Acoustic Targets. Wave Motion,1984,6:501-516
[10]王勖成,邵敏编著.有限元法基本原理和数值方法.第二版.北京：清华大学出版社.1999
[11]徐植信.弹性波传播理论一些问题的研究现状和展望.上海力学.1989,10(3)：6-10页
[12]王仁等.第十九届国际理论与应用力学大会(ICTAM)情况介绍.力学与实践,1997,19(1)：57-64
[13]胡聿贤、周锡元.地震工程跨世纪发展趋势.工程抗震,1999(1)：3-9
[14]王铎、汪越胜.界面动力学研究近况.上海力学,1993(4)：1-15
[15]刘殿魁,田家勇.SH波对界面圆柱形弹性夹杂散射及动应力集中.爆炸与冲击.1999,19(2)：115-123页
[16]Yang Zailin, Liu Diankui. Scattering far field solution of SH-wave by
[16]Yang Zailin, Liu Diankui. Scattering far field solution of SH-wave by movable rigid cylindrical interface. Acta Mechanica Solida Sinica,2002, 15(3):214-220P
[17]刘殿魁,林宏.SH波对双相介质界面附近圆形孔洞的散射.固体力学学报.2003,24(2)：197-204页
[18]Chen Zhigang, Liu Diankui and Yang Zailin. Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity. Earthquake Engineering and Engineering Vibration,2003, Vol2, No.2: 299-306P
[19]黄克智,徐秉业.固体力学发展趋势.北京：北京理工大学出版社,1995：33-45页
[20]郑哲敏,周恒,张涵信,黄克智,白以龙.21世纪初的力学发展趋势.力学进展,1995,25(4)：433-449页
[21]刘晶波.波动的有限元模拟及复杂场地对地震动的影响.国家地震局工程力学研究所博士学位论文.1989
[22]林成森编著.数值计算方法(下册).科学出版社,1999：60-95页
[23]廖振鹏、杨光.稳态SH波动的有限元模拟,地震学报,1994,16(1)：96-105
[24]廖振鹏、刘晶波.波动有限元模拟的基本问题.中国科学,1992,B辑(8)：875-883
[25]廖振鹏.工程波动理论导论.北京：科学出版社,2002
[26]刘晶波、廖振鹏.离散网格中的弹性波动(Ⅱ)-几种有限元离散模型的对比分析.地震工程与工程振动,1989,9(2)：1-14
[27]刘晶波、廖振鹏.有限元离散模型中得出平面波动.力学学报,1992,24(2)：208-215
[28]黎在良、刘殿魁.固体中的波.北京：科学出版社,1995
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