含切口的压电准晶组合结构界面断裂分析的辛-等几何耦合方法
Symplectic Isogeometric Analysis Coupling Method for Interfacial Fracture of Piezoelectric Quasicrystal Composites With Notches
杨震霆 1王雅静 1聂雪阳 1徐新生 1周震寰1
作者信息
- 1. 大连理工大学 工程力学系 工业装备结构分析优化与CAE软件全国重点实验室,辽宁 大连 116024
- 折叠
摘要
发展了一种适用于含有切口的压电准晶/压电晶体/弹性体三材料组合结构界面断裂问题的高精度的半数值半解析方法.首先,通过引入Hamilton体系建立了三材料组合结构的Hamilton对偶方程,将原问题在传统 La-grange体系下的高阶偏微分控制方程转化为低阶常微分方程组.其次,通过分离变量法求解问题对应的辛本征值和本征解,将各物理场变量利用辛级数展开形式表示.最后,将辛级数与等几何分析方法相结合,获得了辛-等几何耦合列式,直接求得切口尖端附近奇异物理场及其强度因子的解析表达式.
Abstract
A high-precision semi numerical and semi analytical method for interfacial fracture problem of piezo-electric quasicrystals(PQCs)/piezoelectric crystals(PZCs)/elastic material composites with notches was de-veloped.Firstly,the Hamiltonian system was introduced and the Hamiltonian dual equations for the 3-material composite were formulated.The higher order partial differential governing equations were transformed into a set of ordinary differential equations.Secondly,the symplectic eigenvalues and eigensolutions were obtained through separation of variables.The physical quantities were expressed with the expansion of symplectic series.Finally,a symplectic isogeometric analysis(IGA)coupling equation was derived through combination of the symplectic series and the IGA.The analytical expressions of the physical quantities near the notch tip and the intensity factors were derived.
关键词
准晶体/压电材料/等几何分析/Hamilton体系/V形切口/界面断裂Key words
quasicrystal/piezoelectric material/isogeometric analysis/Hamiltonian system/V notch/interfa-cial fracture引用本文复制引用
基金项目
辽宁省自然科学基金(2023-MS-118)
出版年
2024
国家科技期刊平台
NSTL
万方数据