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

作　　者：杨震霆 王雅静 聂雪阳 徐新生[1] 周震寰[1] YANG Zhenting;WANG Yajing;NIE Xueyang;XU Xinsheng;ZHOU Zhenhuan(State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China)

机构地区：[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

出　　处：《应用数学和力学》2024年第2期144-154,共11页Applied Mathematics and Mechanics

基　　金：辽宁省自然科学基金(2023-MS-118)。

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Lagrange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.A high-precision semi numerical and semi analytical method for interfacial fracture problem of piezoelectric quasicrystals(PQCs)/piezoelectric crystals(PZCs)/elastic material composites with notches was developed.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 

分 类 号：O346[理学—固体力学]