General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics  

作　　者：Jing YU Junhong GUO Ernian PAN Yongming XING 

机构地区：[1]School of Science, Inner Mongolia University of Technology [2]College of General Education, Inner Mongolia Normal University [3]Department of Civil Engineering, University of Akron

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第6期793-814,共22页应用数学和力学（英文版）

基　　金：Project supported by the National Nature Science Foundation of China(Nos.11262012,11262017,11462020,and 10761005);the Scientific Research Key Program of Inner Mongolia University of Technology(No.ZD201219)

摘　　要：Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.

关 键 词：quasicrystals （QCs） piezoelasticity fracture mechanics CRACK complexvariable method 

分 类 号：O346.1[理学—固体力学]