文档介绍：
压电双材料基体裂纹瞬态响应的时域边界
元分析#
雷钧,杨庆生*
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(北京工业大学机械工程与应用电子技术学院,北京 100124)
摘要:本文采用时域边界元法对力电平面冲击载荷作用下双层压电材料中基体裂纹的瞬态响
应问题进行了数值研究。针对典型的双材料模型,采用子域法沿界面将双材料裂纹体分成两
个均匀子域,分别对子域的外边界应用时域位移边界积分方程;对裂纹面应用超强奇异时域
面力边界积分方程。时间域采用 Lubich 公式对时间卷积进行求积;空间域采用配点法进行
插值求积。通过位移插值法确定裂尖动态应力强度因子与电位移强度因子。算例研究了加载
组合、裂纹位置、材料组合等参数对裂尖动态强度因子以及能量释放率的影响规律。
关键词:时域边界元法;裂纹;动态强度因子;压电双材料
中图分类号:O341
Transient response of subinterface cracks in piezoelectric
bi-materials by time-domain BEM
LEI Jun, YANG Qingsheng
(College of Mechanical Engineering and Applied Electronics Technology,Beijing University Of
Technology, Beijing 100124)
Abstract: A time-domain boundary element method (BEM) together with the sub-domain
technique is applied to study transient response of a sub-interface crack in piecewise homogeneous
linear piezoelectric bi-materials under mechanical and electrical impacts. For each sub-domain,
the traditional displacement boundary integral equations (BIEs) and the hypersingular traction
BIEs are applied on the external boundary and the crack faces. The present time-domain BEM
uses a quadrature formula for the temporal discretization to approximate the convolution integrals
and a collocation method for the spatial discretization. Quadratic quarter-point elements are
implemented at the crack tips. A displacement extrapolation technique is used to determine the
dynamic stress intensity factors (DSIFs) and dynamic electrical displacement intensity factor
(DEDIF). Numerical examples are presented and discussed to demonstrate the accuracy and the
efficiency of the present time-domain BEM and the effects of loading and bination
and geometric conﬁguration on DSIFs, DEDIF and the dynamic energy release rate (DERR).
Keywords: time-domain boundary element method; crack; dynamic intensity factors; piezoelectric
bi-materials
0 引言
压电材料由于具有独特的力电耦合效应,作为换能器、传感器和驱动器等在智能结构中
得到广泛应用。然而由于压材料固有的脆性,在极化和使用过程中,介质中会出现许多弥散
分布的微裂纹、分层、空洞或夹杂等缺陷。而实际应用中很多元器件处于动态耦合载荷的工
作环境,在