The plane strain analysis for one-dimensional hexagonal piezoelectric quasicrystals strip in aperiodical plan

2018 International Conference on Civil, Architecture and Disaster Prevention

土木建筑工程

Guo, Huaimin^1 ; Gao, Ming^1 ; Zhao, Guozhong^1 ; Jiang, Lijuan^2

Mathematics Science, Bao Tou Teacher's College, Bao Tou

014030, China^1

Education Science, Bao Tou Teacher's College, Bao Tou

014030, China^2

关键词: Crack problems;    Fracture problems;    Isotropic piezoelectric materials;    Physical equations;    Plane strain analysis;    Quasi-periodic;    Stress potential;    Stress-strain relationships;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/218/1/012072/pdf
DOI  :  10.1088/1755-1315/218/1/012072

学科分类：土木及结构工程学

来源: IOP

【 摘 要 】

A new stress potential function is introduced, the non periodic plane problem in one-dimensional hexagonal piezoelectric quasicrystals is discussed and the physical equation of the stress-strain relationship in the non periodic plane is constructed. The exact solution of the straight crack in the periodic direction of the one-dimensional hexagonal piezoelectric quasicrystal is obtained. As an application, the problem of straight crack perpendicular to the direction of quasi-periodical in one-dimensional hexagonal piezoelectric quasicrystal with long and narrow body is solved. When the width of the long body becomes infinitely large, the Griffith crack solution is obtained. The results show that the stress at the crack tip remains singularity, which is basically consistent with the crack problem that penetrates along the quasi periodic direction. When the phonon field and the phase field get to zero, the above analytical solution degenerates into the fracture problem of isotropic piezoelectric materials, the results are in agreement with the existing results.