Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

doi:10.1007/s11709-020-0617-4

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (3) : 632-645 https://doi.org/10.1007/s11709-020-0617-4

RESEARCH ARTICLE

Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU^1,², Kezhen YAN¹(

), Jianhong MAN¹, Nengyuan LIU¹

¹. College of Civil Engineering, Hunan University, Changsha 410082, China
². Department of Civil and Environmental Engineering, Michigan Technological University, Houghton, MI 49931, USA

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Abstract

A better understanding of the mechanical behavior of the multi-layered structure under external loading is the most important item for the structural design and the risk assessment. The objective of this study are to propose and develop an analytical solution for the mechanical behaviors of multi-layered structure generated by axisymmetric loading, and to investigate the impact of anisotropic layers and interlayer conditions on the multi-layered structure. To reach these objectives, first, according to the governing equations, the analytical solution for a single layer was formulated by adopting the spatial Hankel transform. Then the global matrix technique is applied to achieve the analytical solution of multi-layered structure in Hankel domain. The sliding and bonded interlayer conditions were considered in this process. Finally, the numerical inversion of integral transform was used to solve the components of displacement and stress in real domain. Gauss-Legendre quadrature is a key scheme in the numerical inversion process. Moreover, following by the verification of the proposed analytical solution, one typical three-layered flexible pavement was applied as the computing carrier of numerical analysis for the multi-layered structure. The results have shown that the anisotropic layers and the interlayer conditions significantly affect the mechanical behaviors of the proposed structure.

Keywords multi-layered structure Hankel transformation anisotropic transversely isotropic interlayer condition Gauss-Legendre quadrature

Corresponding Author(s): Kezhen YAN

Just Accepted Date: 11 April 2020 Online First Date: 25 May 2020 Issue Date: 13 July 2020

Cite this article:

Lingyun YOU,Kezhen YAN,Jianhong MAN, et al. Anisotropy of multi-layered structure with sliding and bonded interlayer conditions[J]. Front. Struct. Civ. Eng., 2020, 14(3): 632-645.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0617-4
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I3/632

Fig.1 Sketch of the studied interlayer between layer-i and layer-(i + 1).

Fig.2 Vertical displacements comparison with the example in Ref. [⁵⁹].

Fig.3 Radial stresses comparison with results from BISAR 3.0.

Tab.1 Model parameters used in comparisons [³⁷]

response	top layer-3		top layer-2	top layer-1
response	$σ z$ (MPa)	$ε z$ (1E–6)	$ε z$ (1E–6)	$δ z$ (mm)
average measured	0.068	2000	580	0.4318
GT-PAVE (40 ksi)	0.074	2112	408	0.4318
present solution	0.070	2095	496	0.4064

Tab.2 Response variable comparison with measured results from Ref [³⁷].

Tab.3 Properties of the elastic layers for multi-layered structure

Tab.4 The combination cases of interlayer condition and modulus ratio

Fig.4 Vertical displacement of top-surface versus radial distance.

Fig.5 Radial stress versus structure depth.

Fig.6 Horizontal shear stress versus structure depth.

Fig.7 Impact of transversely isotropic properties on maximum displacements: (a) transversely isotropic of layer-1 and (b) transversely isotropic of layer-2.

Fig.8 Impact of transversely isotropic properties on maximum radial stresses: (a) transversely isotropic of layer-1 and (b) transversely isotropic of layer-2.

Fig.9 Impact of transversely isotropic properties on maximum horizontal shear stresses: (a) transversely isotropic of layer-1 and (b) transversely isotropic of layer-2.

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