正交各向异性材料热弹性问题的三维无网格法计算模型及应用

建立了正交各向异性材料热弹性问题的三维无网格伽辽金(Element Free Galerkin, EFG)法计算模型。利用该计算模型对三维复合材料汽轮机叶轮和轴承座进行了热弹性分析,对比了材料方向角及热导率因子、热膨胀系数因子和拉压弹性模量因子不同组合情况下轴承座的最大热变形总位移和当量应力值,讨论了材料方向角及上述正交各向异性因子对热变形和当量应力的影响规律,并与各向同性材料进行了对比。结果表明:三维EFG模型的热变形总位移和当量应力相对误差范数分别比有限元法小0.1215%和0.1359%;材料方向角同时影响热变形的大小和方向,但对当量应力方向影响不大;正交各向异性材料因子主要影响热变形和当量应力的大小。在考虑热-机械载荷作用下的三维复合材料零件结构设计中,当以刚度或强度为主要需求时,材料方向角、热导率因子、热膨胀系数因子、拉压弹性模量因子分别在(45°~60°,8:1:4~10:1:5,(1/6):(1/5):1~(1/5):(1/4):1,(7/5):1:(9/5)~(3/2):1:2)或(0°~10°,(1/10):1:(1/5)~(1/8):1:(1/4),(1/5):1:(1/6)~(1/4):1:(1/5),1:(1/5):(1/10)~1:(1/4):(1/8))范围内取值能有效降低轴承座等结构的热变形和当量应力。     

Analysis of plane waves in anisotropic thermoelastic diffusive medium

This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.     

Exactly solvable spherically anisotropic thermoelastic microstructures

Microstructures possessing local spherical anisotropy are considered in this paper. An example is a spherulitic polymer which can be modelled by an assemblage of spheres of all sizes in which a radial direction in every sphere is an axis of local transverse isotropy. Our purpose is to construct effectively isotropic microstructures, with spherically anisotropic and thermoelastic constituents, whose effective bulk modulus, thermal stress and specific heat can be exactly determined. The basic microstructure for which this is achieved in the present paper is the nested composite sphere assemblage of Milgrom and Shtrikman (J. Appl. Phys. 66 (1989) 3429) which was originally formulated for isotropic constituents, in the settings of conductivity and coupled fields with scalar potentials. Here, we allow the phases of this microstructure to be spherically thermoelastic with a symmetry class which can be trigonal, tetragonal, transversely isotropic, cubic or isotropic with respect to a local spherical coordinate system. A rich class of new exact results for two-phase composites and polycrystals are obtained.     

弹性、热弹性物性值反问题的边界元分析

本文采用边界元法和卡尔曼滤波,对弹性、热弹性问题物性值进行反分析,由有限个观测点的位移值,同时反算出材料的拉压弹性模量Ε、泊桑比ν和线膨胀系数α。     

Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal–mechanical connections

This work examines the overall thermoelastic behavior of solids containing spherical inclusions with surface effects. Elastic response is evaluated as a superposition of separate solutions for isotropic and deviatoric overall loads. Using a variational approach, we construct the Euler–Lagrange equation together with the natural transition (jump) conditions at the interface. The overall bulk modulus is derived in a simple form, based on the construction of neutral composite sphere. The transverse shear modulus estimate is derived using the generalized self-consistent method. Further, we show that there exists an exact connection between effective thermal expansion and bulk modulus. This connection is valid not only for a composite sphere, but also for a matrix-based composite reinforced by many randomly distributed spheres of the same size, and can be viewed as an analog of Levin’s formula for composites with surface effects.     

Optimisation de renforts composites internes de structures tridimensionnelles

The reinforcement of a 3D structure with composite panels is considered. The behaviour of those panels are to be optimized considering the external loading of the 3D structure. The study is within the framework of anisotropic linear elasticity. The 3D model takes into account the rigidity induced by Kirchhoff–Love plate reinforcement. An optimization of the behavior characteristics of the composite reinforcement (density and orientation of fibers at each point) is presented.     

Elliptical inclusion in an anisotropic plane: non-uniform interface effects

We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion. In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale, we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus. As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform (described by a constant interface stretching modulus for the entire interface), the anisotropic case considered here necessitates non-uniform effects of interface elasticity (described by a non-constant interface stretching modulus), because the bulk surrounding the interface is anisotropic. To this end, we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface. We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix, which is applicable to the arbitrary orientation and aspect ratio of the inclusion, an arbitrarily variable interface modulus, and an arbitrary uniform external loading applied remotely. The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples. It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion.     

THE EFFECT OF DUAL-PHASE-LAG MODEL ON REFLECTION OF THERMOELASTIC WAVES IN A SOLID HALF SPACE WITH VARIABLE MATERIAL PROPERTIES

The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.     

Thermal expansion of polycrystalline aggregates: II. Self consistent approximation

The Self Consistent Scheme approximation method is applied to evaluate the thermal expansion coefficient of statistically isotropic polycrystalline aggregates, in terms of single crystal thermoelastic properties and polycrystal elastic properties. The case of orthorhombic crystals is considered in detail.     

Determining the effective thermoelastic characteristics of regularly laminated composite in the asymmetric theory of elasticity

The asymmetric theory of elasticity is used to model a hybrid laminated composite of regular structure with all phases isotropic. The effective thermoelastic characteristics of the composite are determined. It is shown that the equations derived can be used to determine stress–strain state in all the phases of the composite using the average components of the tensors of force stresses, couple stresses, strains, and wryness in a layered material, which is of fundamental importance for the design of composites based on structural theories of failure     

Thermoelastic stresses in SiC single crystals grown by the physical vapor transport method

A finite element-based thermoelastic anisotropic stress model for hexagonal silicon carbide polytype is developed for the calculation of thermal stresses in SiC crystals grown by the physical vapor transport method. The composite structure of the growing SiC crystal and graphite lid is considered in the model. The thermal expansion match between the crucible lid and SiC crystal is studied for the first time. The influence of thermal stress on the dislocation density and crystal quality is discussed. The project supported by the National Natural Science Foundation of China (10472126) and the Knowledge Innovation Program of Chinese Academy of Sciences. The English text was polished by Keren Wang     

考虑热渗效应的有限长圆柱热固结解

在作者已建立的饱和多孔介质耦合非线性热弹性理论基础上,考虑热渗效应,建立了饱和多孔介质耦合热弹性固结方程,并推导了有限长圆柱热固结问题的解析解,进而以温控三轴试验的试样为例进行了算例分析,同时利用COMSOL软件进行了数值模拟,并将解析结果和数值结果进行对比．结果表明：在不排水条件下,影响试样最终孔压大小的参数是：土的泊松比>弹性模量>水的体膨胀系数,渗透系数对孔压变化影响不大,考虑与不考虑水土压缩性不影响孔压的计算;相对线弹性情况,考虑非线弹性膨胀系数随温度变化时的孔压有所下降,轴向应变变化很小．     

On the thermostatics of composite materials

The problem of determining overall thermoelastic moduli of some solid composites is discussed. The phases may be arbitrarily anisotropic. One phase is required to be a matrix and the remainder are required to be aligned ellipsoidal inclusions. The volume concentrations are arbitrary. Some exact results are obtained for a binary composite. In the general case the self-consistent method is used to estimate the overall moduli. The general results are shown to reduce to those known for an isotropic dispersion of spheres.     

Magneto-thermoelasticity for an infinite body with a spherical cavity and variable material properties without energy dissipation

The model of generalized thermoelasticity proposed by Green and Naghdi, is applied to study the electromagneto–thermoelastic interactions in an infinite perfectly conducting body with a spherical cavity. The modulus of elasticity are taking as linear function of temperature. By means of the Laplace transform and Laplace inversion, the problem is solved. The closed form solutions for displacement, temperature, and thermal stresses are represented graphically. A comparison is made with the results in the case of temperature-independent.     

On effective thermal expansion coefficients of composites with anisotropic phases

Bounds on thermal expansion coefficients of composite materials with anisotropic phases are derived using extremum principles of thermoelasticity. Numerical results are presented for two-phase composites with isotropic and orthotropic phases.     

Bounds of the expansion coefficients of composites reinforced by spherically isotropic particles

I.IntroductionProblemsconcerningrigorousboundsofeffectivepropertiesofheterogeneousmediahaveattractedgreatattentionforalongtime.HashinandShtrikmannlllgavethebestpossiblelowerandupperboundsoftheeffectiveelasticmoduliofcompositesconsistingoftwoisotropicphase…     

Elastic bending analysis of bilayered beams by an alternative two-variable method

An alternative two-variable method is used to reanalyze thermoelastic bending problems of bilayered beams subjected to external moments and internal stresses. The differences among zero-stress axis, zero-strain axis (i.e. neutral axis), bending axis, centroidal axis, and the parameter conditions for null/single/dual zero-stress axes are investigated analytically and numerically. Comparisons of thermoelastic stress predictions by the present model with Stoney's model and Hsueh's model are discussed in a representative case of GaAs top coat/Si substrate wafers. Results showed that the neutral axis does not coincide with the zero-stress axis in the general case, and the numbers and the locations of zero-strain or zero-stress axes depend on not only elastic modulus, thickness and/or thermal expansion coefficient ratios between the film and the substrate but also mechanical/thermal loading ratio.     

Thermal expansion of polycrystalline aggregates: I. Exact analysis

An exact relation is developed between the thermal expansion coefficient and the bulk modulus of statistically isotropic polycrystalline aggregates composed of crystals of hexagonal, tetragonal or trigonal symmetry. This relation is exploited to derive simple close bounds for the thermal expansion coefficient in terms of single crystal properties. Comparison of bounds to experimentally obtained expansion coefficients shows fair to very good agreement.     

采用瓣叶复合材料的生物心脏瓣膜的力学分析

采用微观组织结构分析及宏观复合材料分析结合的方法,分析了猪主动脉瓣的非线性复合材料性质,提出了一种适用于猪主动脉瓣的非线性复合材料本构模型,用提出的非线性复合材料本构模型,对闭合承载状态下的等厚度与变厚度几何模型的猪主动脉瓣的应力分布及变形进行了有限元数值模拟,发现：与各向同性瓣叶相比,单向增强复合材料的瓣叶不但具有较强的承载能力,而且具有较大的柔软性。