Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures

doi:10.1007/s10915-019-01041-x

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	Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures
	Ma, Qiang 1; Wang, Hao 1; Yang, Zhiqiang 2; Li, Zhihui 3,4; Cui, Junzhi 5
	2019-11-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	81 期号:2 页码:689-731
摘要	The second-order coupled piezoelectric models based on the multi-scale asymptotic expansion method are developed for the axially and spherically symmetric composites. The governing piezoelectric equations are compactly formulated in cylindrical and spherical coordinates, and the composite domains are assumed to be periodically occupied by the representative cells. The multi-scale asymptotic expansions for the displacement and the electric potential are formally defined and the effective elastic, piezoelectric, and dielectric coefficients are expressed in terms of the microscopic functions defined on the cell domain. Particularly, the cell solutions and the homogenized solutions for the plane axisymmetric and spherically symmetric problem are derived analytically. The corresponding finite element procedure is proposed, in which the Newmark algorithm is applied to construct the computational scheme in the temporal domain. Numerical experiments are carried out to simulate both the static and dynamic asymptotic behavior of the space axisymmetric and the one-dimensional plane axisymmetric structures. It is validated from the numerical examples that the asymptotic models proposed in the current work are effective to capture the macroscopic performance of the piezoelectric structures and the second-order expansions of the solutions is essential for obtaining the correct distributions of the stress and electric displacement.
关键词	Axially and spherically symmetric piezoelectricity Periodic composite materials Multi-scale expansion homogenization method Second-order asymptotic approximation Finite element simulation
DOI	10.1007/s10915-019-01041-x
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11801387] ; National Natural Science Foundation of China[11501389] ; National Natural Science Foundation of China[11471214] ; State Key Laboratory of Science and Engineering Computing ; fundamental research funds for the central universities
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000491440200004
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50682
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Hao; Yang, Zhiqiang
作者单位	1.Sichuan Univ, Sch Math, Chengdu 610065, Sichuan, Peoples R China 2.Harbin Inst Technol, Dept Astronaut Sci & Mech, Harbin 150001, Heilongjiang, Peoples R China 3.China Aerodynam Res & Dev Ctr, Hyperveloc Aerodynam Inst, Mianyang 621000, Sichuan, Peoples R China 4.BUAA, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China 5.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ma, Qiang,Wang, Hao,Yang, Zhiqiang,et al. Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,81(2):689-731.
APA	Ma, Qiang,Wang, Hao,Yang, Zhiqiang,Li, Zhihui,&Cui, Junzhi.(2019).Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures.JOURNAL OF SCIENTIFIC COMPUTING,81(2),689-731.
MLA	Ma, Qiang,et al."Second-Order Asymptotic Analysis and Computations of Axially and Spherically Symmetric Piezoelectric Problems for Composite Structures".JOURNAL OF SCIENTIFIC COMPUTING 81.2(2019):689-731.