Bending Analysis of Functionally Graded One-Dimensional Hexagonal Piezoelectric Quasicrystal Multilayered Simply Support
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ISSN 1860-2134
Bending Analysis of Functionally Graded One-Dimensional Hexagonal Piezoelectric Quasicrystal Multilayered Simply Supported Nanoplates Based on Nonlocal Strain Gradient Theory Li Zhang1
Junhong Guo1,2
Yongming Xing1
1
( Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China) (2 School of Aeronautics, Inner Mongolia University of Technology, Hohhot 010051, China)
Received 26 August 2020; revision received 29 October 2020; Accepted 30 October 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT In this study, the nonlocal strain gradient theory is adopted to investigate the static bending deformation of a functionally graded (FG) multilayered nanoplate made of onedimensional hexagonal piezoelectric quasicrystal (PQC) materials subjected to mechanical and electrical surface loadings. The FG materials are assumed to be exponential distribution along the thickness direction. Exact closed-form solutions of an FG PQC nanoplate including nonlocality and strain gradient micro-size dependency are derived by utilizing the pseudo-Stroh formalism. The propagator matrix method is further used to solve the multilayered case by assuming that the layer interfaces are perfectly contacted. Numerical examples for two FG sandwich nanoplates made of piezoelectric crystals and PQC are provided to show the influences of nonlocal parameter, strain gradient parameter, exponential factor, length-to-width ratio, loading form, and stacking sequence on the static deformation of two FG sandwich nanoplates, which play an important role in designing new smart composite structures in engineering.
KEY WORDS Nonlocal strain gradient theory, Functionally graded material, Quasicrystal, Multilayered nanoplates, Propagator matrix method
1. Introduction Quasicrystals (QCs), as firstly discovered by Shechtman in rapidly cooled Al-Mn alloys, possess a long-range order without translational periodicity [1]. In order to describe the unique atomic configuration, QCs in the real three-dimensional physical space may be seen as a projection of a periodic lattice in the higher-dimensional mathematical space. The projection of the periodic lattice in four-, five-, and six-dimensional space to the physical space generates one-, two-, and three-dimensional QCs, respectively. To date, over 100 kinds of QCs have been developed, such as the QC alloys based on aluminum, copper, magnesium, nickel, titanium, and zinc. According to the QC elastic energy theory, there are two elementary excitations, i.e., the phonon and phason fields, which describe the classical motion of atoms in crystals and the arrangements of atomic configurations along the quasi-periodic direction, respectively. Once QCs are discovered, some physical properties, such as the structural, electronic, magnetic, optical, and thermal properties, have been investigated extensively. Among many
Corresponding authors. E-mails: [email protected]; [email protected]
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