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2018 Vol. 39, No. 1 Published: 2018-02-28

	1	Research Progress in Multi-scale Mechanics of Composite Materials ^Hot!

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.030
		Multi-scale mechanics of composite materials is the subject that studies mechanical properties of inhomogeneous materials by the means of multi-scale analysis. In recent years, significant progress has been achieved in micro- and nano-scale experimental techniques, and many new types of advanced materials with multiple phases and hierarchical structures have been proposed and even produced, which both greatly promote the development of multi-scale mechanics of composite materials. In order to present important approaches and current developments in the multi-scale analysis for mechanical properties of inhomogeneous materials, first, the classical and commonly-used theoretical approaches are reviewed in this paper from nano and micro scales to macro scale, and subsequently, the multi-scale computational methods are introduced for both heterogeneous continuum and discrete systems. In addition, some research examples are presented to show how to use the theoretical and computational multi-scale methods to analyze complex material systems, including the studies of authors’ group in nanocomposite materials, impact-resistant energy absorbing materials, network materials and hierarchical self-similar materials. Finally, some future study directions of multi-scale mechanics for inhomogeneous materials are prospected.
		2018 Vol. 39 (1): 1-68 [Abstract] ( 794 ) HTML (1 KB) PDF (0 KB) ( 505 )

	69	Reliability-based Topology Optimization Considering Spatially Varying Uncertain Material Properties ^Hot!
	Reliability-based Topology Optimization Considering Spatially Varying Uncertain Material Properties[J]. journal1, 2018,39(1): 69-79')" href="#">
		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.016
		Topology optimization aims to find the optimal distribution of a given amount of material in a design domain to maximize the structural performance. However, the deterministic topology optimization may generate a structural design that is not reliable or robust under uncertain parameter variations. The reliability-based topology optimization considering spatially varying uncertain material properties is developed in this paper. In practical engineering, some uncertain parameters fluctuate not only over the time domain but also in space. Therefore, an independent random variable is incapable of characterizing the structural uncertainty due to its spatially varying nature. In such circumstances, we introduce a random field model for the spatially varying physical quantities. The elastic modulus is modeled as a random field with a given probability distribution, which is discretized by means of an Expansion Optimal Linear Estimation (EOLE). The response statistics and their sensitivities are evaluated with the polynomial chaos expansions (PCE). The accuracy of the proposed method is verified by the Monte Carlo simulations. The reliability of the structure is analyzed using the first-order reliability method (FORM). Two approaches to solving the optimization problems are compared, which are the double-loop approach and the sequential approximate programming (SAP) approach. Numerical examples show that the proposed method is valid and efficient for both 2D and 3D topology optimization problems. The obtained results show that the SAP approach has higher efficiency than the double-loop approach, and can realize concurrent convergence of topology optimization and reliability analysis. In addition, it is found that the reliability-based topology optimization (RBTO) solutions considering the uncertain model (the random variable and the random field model) have different topologies and member sizes to improve the level of reliability as compared with the deterministic solutions. Also, the optimal designs considering the random field model require less material, compared with those obtained with random variables.
		2018 Vol. 39 (1): 69-79 [Abstract] ( 394 ) HTML (1 KB) PDF (0 KB) ( 455 )

	80	Wave Input Method for Three-dimensional Wave Scattering Simulation of an Incident Wave in an aAbitrary Direction ^Hot!
	Wave Input Method for Three-dimensional Wave Scattering Simulation of an Incident Wave in an aAbitrary Direction[J]. journal1, 2018,39(1): 80-89')" href="#">
		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.013
		The realization of artificial boundary condition and wave input are the key factors for the numerical simulation of wave scattering in semi-infinite domain. To determine the wave input, the one-dimensional or two-dimensional free-field problems have been analyzed for vertically-incident plane waves or obliquely-incident waves in the direction parallel to the plane of the two axes, which, however, cannot account for an incident wave in an arbitrary direction in the three-dimensional problems and limits the applications. A feasible method to solve the input of an incident plane seismic wave in an arbitrary direction is proposed in this paper. First, the two-dimensional free-field problem is analyzed through the Thomson-Haskell transfer matrix method. Then, the three-dimensional free-field motion is obtained through the transformation between two coordinate systems. Combined with the lumped-mass explicit finite element method (FEM), the input for transmitting boundary and viscous-spring artificial boundary are realized. The method is verified and the effect of incident angle is demonstrated through numerical examples.
		2018 Vol. 39 (1): 80-89 [Abstract] ( 211 ) HTML (1 KB) PDF (0 KB) ( 373 )

	90	Stress Concentration Analysis of an Arbitrarily Shaped Hole Coated with a Functionally Graded Layer ^Hot!
	Stress Concentration Analysis of an Arbitrarily Shaped Hole Coated with a Functionally Graded Layer [J]. journal1, 2018,39(1): 90-99')" href="#">
		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.011
		A general solution of the stress concentration in a homogeneous plate with an arbitrary shape hole coated by a functionally graded layer is presented under the remote uniform loads. With using the method of piece-wise homogeneous layers, the functionally graded layer in which the material properties change continuously along the normal direction of the hole is approximately decomposed to N homogeneous layers. When N is chosen to be large enough, the material constants in each layer can be regarded as unchanged. By means of the technique of conformal mapping, N homogeneous layers in -plane are transformed into N concentric circular rings in -plane, and then the complex potentials in each circular ring and the plate in -plane can be given in the form of series with unknown coefficients based on the theory of the complex variable functions. The stress and displacement continuous conditions on the interfaces of each homogeneous layer are used to produce a set of linear equations containing all the unknown coefficients. Through solving these linear equations, the complex potentials can be finally obtained in each layer and the plate. Numerical results of stress distribution around the holes with various shapes including circle, ellipse, triangle, square, rectangle etc. are presented for different varying Young’s modulus. It is shown that the stress concentrations around the elliptical and rectangle holes are more obvious than those of circular and square holes, respectively, and the most obvious one is triangle hole. Moreover, it is most important that the influence of the gradient exponent of Young’s modulus on the stress distributions is noticeable for all shape holes, and the stress concentrations decrease remarkably as the exponent value increases. Therefore, it can be concluded that the existence of the functionally graded layer influence obviously the stress distribution around the holes with various shapes, and the stress concentration can be effectively reduced by choosing proper change ways of the normal elastic properties in the functionally graded layer.
		2018 Vol. 39 (1): 90-99 [Abstract] ( 313 ) HTML (1 KB) PDF (0 KB) ( 379 )

	100	Equivalent Moduli of Accordion Honeycomb with Zero Poisson’s Ratio

		DOI: 10.19636/j.cnki.cjsm42-1250/o3.2017.017
		Flexible skin is an essential component of morphing wing and morphing wind turbine blade. The support structure of the flexible skin undergoing one-dimensional morphing is required of good in-plane morphing capability and good out-of-plane load-bearing capability as well as zero Poisson’s ratio. To overcome these problems, an accordion honeycomb with zero Poisson’s ratio was proposed as a potential candidate for support structure of one-dimensional morphing flexible skin. To comprehensively analyze the in-plane and out-of-plane elastic properties of the proposed structure, the equivalent elastic modulus in the x-direction and the equivalent shear modulus in the x-y plane were derived by the Castigliano’s second theorem considering the internal bending moment, axial force and shear force; the equivalent shear modulus in the x-z plane was determined by principle of minimum complementary energy and principle of minimum potential energy; besides, the equivalent elastic moduli in the y and z direction, and the equivalent shear modulus in the y-z plane were also obtained by conventional derivation methods. The theoretical formulas were then verified by finite element analysis in ANSYS. Finally, comparisons with several conventional theoretical models were carried out to show the superiority of the theoretical model adopted in this paper. Results show that theoretical formulas are of good agreement with finite element analysis, proving the validity of the derivation. Accordion honeycomb of lower in-plane stiffness and higher out-of-plane stiffness will be obtained by employing larger height ratio of inclined beam h, spacing ratio of inclined beam g, thickness ratio of vertical beam η, and smaller thickness ratio t. These results can be used for rapid predictions of the mechanical properties of the accordion honeycomb, providing corresponding reference for structural design of one-dimensional morphing flexible skin. Furthermore, the theoretical model proposed in this paper is more accurate and has a wider range of application on the analyses of similar cellular honeycomb structures than conventional models.
		2018 Vol. 39 (1): 100-112 [Abstract] ( 228 ) HTML (1 KB) PDF (0 KB) ( 511 )

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