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2020年 第41卷 第10期    刊出日期：2020-10-01

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论文

Shear-horizontal waves in periodic layered nanostructure with both nonlocal and interface effects

Ru TIAN, Jinxi LIU, E. N. PAN, Yuesheng WANG

2020, 41(10):  1447-1460.  doi:10.1007/s10483-020-2660-8

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The propagation of shear-horizontal (SH) waves in the periodic layered nanocomposite is investigated by using both the nonlocal integral model and the nonlocal differential model with the interface effect. Based on the transfer matrix method and the Bloch theory, the band structures for SH waves with both vertical and oblique incidences to the structure are obtained. It is found that by choosing appropriate interface parameters, the dispersion curves predicted by the nonlocal differential model with the interface effect can be tuned to be the same as those based on the nonlocal integral model. Thus, by propagating the SH waves vertically and obliquely to the periodic layered nanostructure, we could invert, respectively, the interface mass density and the interface shear modulus, by matching the dispersion curves. Examples are further shown on how to determine the interface mass density and the interface shear modulus in theory.



Elastic interaction between inclusions and tunable periodicity of superlattice structure in nanowires

Yang YANG, Yong NI

2020, 41(10):  1461-1478.  doi:10.1007/s10483-020-2654-6

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The elastic stress distribution and the variation of the elastic energy with spacing between two inclusions of arbitrary sizes in an infinite isotropic cylindrical rod are obtained by an analytical approach and the phase field microelasticity (PFM) simulation. The results show a near-attraction and far-repulsion elastic interaction between two inclusions with hydrostatic dilatation. The critical spacing, at which the interaction changes from attraction to repulsion, is on the order of the radius of the rod, dependent on the length and Poisson's ratio of inclusions. Furthermore, the elastic energy calculations and PFM simulation results indicate that applying the local radial stress on the rod surface can modulate the elastic interaction between inclusions and adjust the periodicity of the superlattice nanowire structure. This can provide some guidelines for the tunable construction of superlattice nanowire structures.

An analytical approach to reconstruction of axisymmetric defects in pipelines using T(0, 1) guided waves

Yihui DA, Bin WANG, D. Z. LIU, Zhenghua QIAN

2020, 41(10):  1479-1492.  doi:10.1007/s10483-020-2661-9

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Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission. Especially, the torsional mode T (0, 1), which is the first order of torsional guided waves, plays the irreplaceable position and role, mainly because of its non-dispersion characteristic property. However, one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy. Taking into account this situation, a quantitative reconstruction method using the torsional guided wave T (0, 1) is proposed in this paper. The methodology for defect reconstruction consists of three steps. First, the reflection coefficients of the guided wave T (0, 1) scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method (HFEM). Then, applying the boundary integral equation (BIE) and Born approximation, the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T (0, 1) and the fundamental solution of the intact pipeline in the frequency domain. Finally, reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain. Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes. Meanwhile, the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated. It is noted that the reconstructive error is less than 10%, providing that the defect depth is no more than one half of the pipe thickness.

The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane

Ming DAI, P. SCHIAVONE

2020, 41(10):  1493-1496.  doi:10.1007/s10483-020-2667-7

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The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials. In anti-plane shear and plane deformations, certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading. Correspondingly, sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of (uniform) remote loading have also been established. In this paper, we demonstrate rigorously that, in all cases, these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.

Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

Yong HUANG

2020, 41(10):  1497-1516.  doi:10.1007/s10483-020-2670-6

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The bending and free vibrational behaviors of functionally graded (FG) cylindrical beams with radially and axially varying material inhomogeneities are investigated. Based on a high-order cylindrical beam model, where the shear deformation and rotary inertia are both considered, the two coupled governing differential motion equations for the deflection and rotation are established. The analytical bending solutions for various boundary conditions are derived. In the vibrational analysis of FG cylindrical beams, the two governing equations are firstly changed to a single equation by means of an auxiliary function, and then the vibration mode is expanded into shifted Chebyshev polynomials. Numerical examples are given to investigate the effects of the material gradient indices on the deflections, the stress distributions, and the eigenfrequencies of the cylindrical beams, respectively. By comparing the obtained numerical results with those obtained by the three-dimensional (3D) elasticity theory and the Timoshenko beam theory, the effectiveness of the present approach is verified.

Size-dependent modal interactions of a piezoelectrically laminated microarch resonator with 3:1 internal resonance

A. NIKPOURIAN, M. R. GHAZAVI, S. AZIZI

2020, 41(10):  1517-1538.  doi:10.1007/s10483-020-2658-6

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The nonlinear interactions of a microarch resonator with 3:1 internal resonance are studied. The microarch is subjected to a combination of direct current (DC) and alternating current (AC) electric voltages. Thin piezoelectric layers are thoroughly bonded on the top and bottom surfaces of the microarch. The piezoelectric actuation is not only used to modulate the stiffness and resonance frequency of the resonator but also to provide the suitable linear frequency ratio for the activation of the internal resonance. The size effect is incorporated by using the so-called modified strain gradient theory. The system is highly nonlinear due to the co-existence of the initial curvature, the mid-plane stretching resulting from clamped anchors, and the electrostatic excitation. The eigenvalue problem is solved to conduct a frequency analysis and identify the possible regions for activating the internal resonance. The effects of the piezoelectric actuation, the electric excitation, and the small-scale effect are investigated on the internal resonance. Exclusive nonlinear phenomena such as Hopf bifurcation and hysteresis are identified in the microarch response. It is shown that by applying appropriate piezoelectric actuation, one is able to activate microarch internal resonance regardless of the initial rise level of the microarch. It is also disclosed that among all the parameters, AC electric voltage has the greatest effect on the energy exchange between the interacting modes. The results can be used to design resonators and internal resonance based micro-electro-mechanical system (MEMS) energy harvesters.

A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

Wei YI, Qiuhua RAO, Wenbo MA, Dongliang SUN, Qingqing SHEN

2020, 41(10):  1539-1560.  doi:10.1007/s10483-020-2653-9

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Based on the elementary solutions and new integral equations, a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries. The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method, the numerical solution of the finite element method, and the analytical-numerical solutions of the series expansion and Laurent series methods. Some numerical examples are presented to investigate the effects of the hole geometry parameters (radii and relative positions) and loading conditions (remote stresses and surface stresses) on the interacting tangential stresses and interacting stress concentration factors (SCFs). The results show that whether the interference effect is shielding (k <1) or amplifying (k> 1) depends on the relative orientation of holes (α) and remote stresses (σ_x^∞, σ_y^∞). When the maximum principal stress is aligned with the connecting line of two-hole centers and σ_y^∞ <0.5σ_x^∞, the plate containing two circular holes has greater stability than that containing one circular hole, and the smaller circular hole has greater stability than the bigger one. This new method not only has a simple formulation and high accuracy, but also has an advantage of wide applications over common analytical methods and analytical-numerical methods in calculating the interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses.

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

Yijie BIAN, Puhao LI, Fan YANG, Peng WANG, Weiwei LI, Hualin FAN

2020, 41(10):  1561-1582.  doi:10.1007/s10483-020-2648-8

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Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption (SEA) capacity. In this paper, square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption (EA) performance. Finite element (FE) simulations of in-plane compression are carried out, and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures. Satisfactory agreement is achieved between the FE simulation results and the theoretical results. It indicates that the 30° oriented lattice has the largest EA capacity. Furthermore, inspired by the polycrystal microstructure of metals, novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together. The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts. This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

Siyu WANG, Lin ZHAN, Huifeng XI, Heng XIAO

2020, 41(10):  1583-1596.  doi:10.1007/s10483-020-2659-7

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A new finite strain elatoplastic J₂-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate. In terms of certain single-variable shape functions representing uniaxial loading and unloading curves, explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys (SMAs) under multiple loading-unloading cycles. Numerical examples show that with only a single parameter of direct physical meaning for each cycle, accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.

Notes on micro-continua exhibiting quantum effects

Heng XIAO

2020, 41(10):  1597-1598.  doi:10.1007/s10483-020-2678-6

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