Hygroelasticity analysis of an elastically restrained functionally graded porous metamaterial circular plate resting on
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2651-7
Hygroelasticity analysis of an elastically restrained functionally graded porous metamaterial circular plate resting on an auxetic material circular plate∗ A. BEHRAVAN-RAD† , M. JAFARI Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran (Received Mar. 7, 2020 / Revised Jun. 5, 2020) Abstract The main objective of this research is to investigate the hygroelastic behavior of a non-homogeneous circular plate made up of porous metamaterial resting on an auxetic material plate. The mechanical properties of the main plate, as well as moisture concentration, vary as an exponential function in the transverse direction. Poisson’s ratio is constant. The elastic supporting medium is developed by considering the structurestructure coupling. Based on the linear hygroelasticity theory, the governing state equations in terms of displacements and moisture concentration are acquired. At first, the Fickian equation is solved to compute the nonlinear distribution of moisture through the plate thickness, and then the state equations are semi-analytically solved using the statespace (SS) method and the differential quadrature (DQ) rule to predict the elastic field quantities. A comprehensive parametric analysis is accomplished to elucidate the effects of key parameters on the steady-state response of the plate under the mechanical and hygral loads. Key words
metamaterial, hygroelasticity, auxeticity, hygral, interaction
Chinese Library Classification O343 2010 Mathematics Subject Classification
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74B05, 74G15
Introduction
Structures composed of advanced composite materials may be exposed to moisture during their operation. When exposed to a hygral environment, they absorb moisture. The mechanical properties of these structures are graded when they are expanded due to moisture absorption. The basic structures (beams, plates, and shells) may be fabricated from heterogeneous materials[1], functionally graded (FG) porous material[2] , auxetic and FG auxetic materials[3–4] , auxetic-porous materials[5] , and inhomogeneous porous metamaterials[6] . The attractive properties of these advanced composite metamaterials have directed researchers to find practical applications in different areas, such as textile, marine, aerospace, and mechanical engineering. ∗ Citation: BEHRAVAN-RAD, A. and JAFARI, M. Hygroelasticity analysis of an elastically restrained functionally graded porous metamaterial circular plate resting on an auxetic material circular plate. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-0202651-7 † Corresponding author, E-mail: [email protected] c Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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A. BEHRAVAN-RAD and M. JAFARI
It is worth noting that the interaction of structure-structure is a prominent topic in contact mechanics. Therefore, with growing the synthesis and production of mechanica
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