混凝土板孔洞反平面动力问题的解析与数值方法

发布时间：2018-03-21 14:12

本文选题：混凝土　切入点：SH波散射　出处：《哈尔滨工程大学》2014年硕士论文　论文类型：学位论文

【摘要】：弹性波动理论对于结构工程中无损检测技术的发展具有重要的意义。混凝土板壳的反平面运动中,由缺陷引起的应力集中问题可以按照带形介质中圆柱孔洞对SH型导波的散射问题来分析。本文主要分为两个部分。在第一部分采用解析方法研究这个问题。首先,构造带形介质中相容导波的形式,即其满足上、下边界应力自由条件。之后,由波函数展开法给出圆形孔洞的散射波的级数表示,根据累次镜像叠加的方法构造由上、下边界反射所形成的相容的散射导波。最后,给定入射导波,由圆柱孔洞边界应力自由的条件来定解波函数级数的系数。数值算例求解了特定导波对圆柱孔洞的散射,给出了圆柱孔洞边沿的动应力分布,讨论了导波阶数、频率以及孔洞位置的影响。在第二部分,选用工程中常见的C30混凝土的各项物理参数,给出一个具体的实例模型。根据有限单元法的基本原理,确定荷载的加载方式,模型的边界条件,有限单元的尺寸以及积分时间步长等参数。分别进行解析方法与数值方法的计算,最后对两者的结果数据进行对比与分析。本文能够丰富弹性动力学中关于反平面应变问题的研究,并为结构检测技术的发展提供理论依据。
[Abstract]:The theory of elastic wave is of great significance for the development of nondestructive testing technology in structural engineering. The problem of stress concentration caused by defects can be analyzed according to the scattering of SH guided waves by cylindrical holes in a strip medium. This paper is mainly divided into two parts. In the first part, analytical methods are used to study this problem. The form of compatible guided waves in a ribbon medium is constructed, that is, it satisfies the free condition of upper and lower boundary stress. Then, the series representation of scattering waves of circular holes is given by the method of wave function expansion, and constructed by the method of repeated image superposition. Finally, given the incident guided wave, the coefficients of the wave function series are determined by the condition of free stress in the boundary of the cylindrical hole. Numerical examples are given to solve the scattering of the cylindrical hole by a particular guided wave. The dynamic stress distribution along the edge of cylindrical hole is given, and the influence of guided wave order, frequency and hole position is discussed. In the second part, the common physical parameters of C30 concrete are selected. A concrete example model is given. According to the basic principle of the finite element method, the loading mode of the load and the boundary conditions of the model are determined. The size and integral time step of finite element are calculated by analytical method and numerical method respectively. Finally, the results are compared and analyzed. This paper can enrich the research on anti-plane strain problem in elastic dynamics and provide the theoretical basis for the development of structural detection technology.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU375.2

【参考文献】