各向异性粘弹性力学的本征化理论

在物体的异性子空间中研究了各向异性粘弹性力学,证明了对粘弹性介质,也存在运动方程及变形协调方程的本征特性,并由此得到相应的模态形式.再利用模态Maxwell本构方程 ,从而提出了一个各向异性粘弹性力学理论.它的优点是:(1) 方程是标量型的,并且各阶之间彼此无关,方程的个数与物体的异性子空间个数相同;(2) 无论物体的各向异性程度如何,其定解方程及相应边界条件形式是统一、显式的;(3)对静力学问题,没有力法和位移法的区别,即在力学空间下,平衡方程和变形协调方程没有区别;(4)每一阶方程都有明确的物理意义,例如在各向同性下,1阶和2阶方程分别代表体积变形过程和剪切变形过程;(5 )在力学空间下,粘弹性力学也存在类似弹性力学的应力势函数,并且它们是非人为确定的 ;(6) 最终解是由各阶解模态叠加构成,适于工程上的近似计算.     

各向异性弹性力学的研究进展

经典的弹性理论主要是研究均匀和各向同性的力学问题。自纳维和哥西在1820年提出弹性理论的基本问题开始,到十九世纪已形成了较为系统而完整的理论,典型的代表性文献是著名的Love著作。各向异性弹性力学的发展与生产发展紧密结合的,本世纪以来,随着航空工业的兴起,胶合木板等新型材料在工业上日益广泛的应用,刺激和推动了这个学科的发展。四十年代中期Lekhnitskii首先总结了苏联学者在三十年代对各向异性体的平面问题     

各向异性弹性力学一般边值问题的广义Stroh公式

当边值问题是简单的,即是应力边值问题时,Stroh公式是很有效的。对于混合边值问题,倒如滑动边界条件,Stroh公式中的简洁的矩阵表达式就失效了。我们提出了一个广义的Stroh公式,它可应用于一大类一般的边界条件。简单的边界条件和滑动边界条件是这一类一般边界条件的特殊情形。值得指出的是,这个关于Stroh公式所作的修正并不大。广义的公式和最后的解答看起来很类似于未修正的原公式和原来的解。然而这个修正却可应用于相当广的边界条件。     

各向异性弹性力学问题Hamilton正则方程的一般形式

本文从修正后的Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，导出了由２１个弹性常数组成的各向异性材料的混合方程，并证明它们即是Ｈａｍｉｌｔｏｎ正则方程。由该统一形式还给出了角铺设材料和正交各向异性材料的Ｈａｎｉｌｔｏｎ正则形式。     

非线性正交各向异性弹性材料的本构方程及其势函数

研究了非线性Green弹性材料弹性张量独立分量,归纳推导出各向异性Green弹性材料、具有一个对称面Green弹性材料、 正交各向异性非线性弹性材料独立的弹性常数个数.从张量函数出发,用含有高阶弹性张量的张量多项式,推导出三阶非线性正交各向异性Green弹性材料本构方程及其势函数.并将本构方程及其势函数用张量不变量,标量不变量表示.证明了方程是完备的,不可约的,满足张量函数表示定理.详细研究Green弹性材料势函数存在的充分和必要条件,给出并证明了具有普适性的势函数存在定理.     

非线性动力系统的规范形系数计算

本文对于ｎ阶一般的非线性动力系统，构造出一种逐项确定其规范形系数的新方法，并有效地用于高阶和高维计算问题。     

非线性模态理论的研究进展

对非线性模态理论的研究进展做了较全面的综述,指出了该领域研究中存在的一些问题和今后的研究方向      

面向剪切下各向异性三相椭圆夹杂中均匀应力

论证了只要合适选择中间界面层的弹性常数，各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场。讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件。所给出的数值算例显示出该结论的正确性。该方法为纤维增强复合材料的设计提供了一条新途径。     

弯曲动脉壁非线性弹性力学性质的理论分析

血管壁非线性力学特性是探索心血管中的血液流动规律及脉搏波传播现象的一个重要前提．在血管力学研究中,直管动脉壁的本构方程已有相当深人的研究,唯独象主动脉弓那样的弯管动脉壁本构方程;至今还没有建立一个理论模型．文中在已有的直管动脉壁本构方程研究基础上,提出一个理论方法来分析弯曲动脉壁的非线性弹性力学性质,在弯曲动脉壁被模拟为均质、正交各向异性、不可压缩材料的前提下,作者从理论上建立了一个表达弯管动脉壁非线性弹性性质的三维ｅ指数型本构方程文中还探讨了弯曲动脉壁内的残余应变分析．     

各向异性非线性强度条件下的边坡稳定性

解释了土体强度各向异性、非线性的物理本质,结合常规直剪试验、三轴试验结果,在前人工作基础上建立了边坡稳定性分析中强度各向异性、非线性的描述方法,其中特别提出了一个各向异性函数．基于Janbu普遍条分法(GPS),运用SPREADSHEET模板程序,提出了一个能将各向异性、非线性强度准则逐点等效到Mohr-Coulomb直线强度准则处理上的迭代方法,准确方便地获得了非线性强度下的边坡稳定性分析．最后的算例展示了方法的使用过程。     

Constitutive Relations of Nonlinear Thermoelasticity of Anisotropic Bodies

Quasilinear relations for finite reversible deformation of anisotropic materials are obtained using a thermomechanical approach. Free energy is written as a function of temperature and compatible invariants of the logarithmic strain measure and basis tensors. Nonlinear thermomechanical effects including different types of material behavior in tension and compression and the temperature dependence of the elastic tensor are taken into account.     

The Remarkable Nature of Radially Symmetric Deformation of Spherically Uniform Linear Anisotropic Elastic Solids

Antman and Negron-Marrero [1] have shown the remarkable nature of a sphere of nonlinear elastic material subjected to a uniform pressure at the surface of the sphere. When the applied pressure exceeds a critical value the stress at the center r=0 of the sphere is infinite. Instead of nonlinear elastic material, we consider in this paper a spherically uniform linear anisotropic elastic material. It means that the stress-strain law referred to a spherical coordinate system is the same for any material point. We show that the same remarkable nature appears here. What distinguishes the present case from that considered in [1] is that the existence of the infinite stress at r=0 is independent of the magnitude of the applied traction σ0 at the surface of the sphere. It depends only on one nondimensional material parameter κ. For a certain range of κ a cavitation (if σ0>0) or a blackhole (if σ0<0) occurs at the center of the sphere. What is more remarkable is that, even though the deformation is radially symmetric, the material at any point need not be transversely isotropic with the radial direction being the axis of symmetry as assumed in [1]. We show that the material can be triclinic, i.e., it need not possess a plane of material symmetry. Triclinic materials that have as few as two independent elastic constants are presented. Also presented are conditions for the materials that are capable of a radially symmetric deformation to possess one or more symmetry planes. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Linear Theory of Porous Elastic Solids

The theory of porous elastic solids with large vacuous interstices, considered by Giovine like materials with ellipsoidal structure, includes, as a particular case, the nonlinear theory of Nunziato and Cowin of elastic materials with small spherical voids finely dispersed in the matrix.In this paper we propose appropriate constitutive relations and then specialize the basic balance equations of Giovine to the linear theory. Also, generalizing the developments of Cowin and Nunziato, we formulate boundary-initial-value problems and examine classical applications as responses to homogeneous deformations and small-amplitude acoustic waves.     

Geometric and Material Nonlinear Static and Dynamic Analysis of Space Truss Structures

A formulation of the nonlinear FEM truss element that takes into account both the geometric nonlinearity and material nonlinearity of the structure is derived. The associated iterative algorithm for the application is described. Based on two inelastic material models (isotropic hardening and dynamic hardening), three space truss structures are subjected to static and to dynamic loads in order to illustrate the application of nonlinear FEM. The nonlinear FEM described can accurately trace the complex structural behavior of space truss structures, including snap-through, and buckling. The FEM results match well with the theoretical results.     

ANISOTROPIC EFFECTS OF QUASI-ISOTROPIC COMPOSITES(I)──MODELLING

Experimental observations show that quasi-isotropic materials, such as N-axial fibre-reinforced composites and woven materials, exhibit various degrees of anisotropy in elasticity and strength, and the anisotropy in strength is normally stronger than that in elasticity. In view of some available experimental data and based on the general formulation of the constitutive equations and failure criteria of quasi-isotropic materials established by using the theory of representations for tensor functions, we postulate several applicable models of the constitutive equations and strength for 3-and 4-axial quasi-isotropic materials to reveal the anisotropic effects. In a continued work (Part II), the anisotropic effect in strength of an infinitely large plate with a single elliptical hole or crack is studied, and the proposed stiffness and strength models are verified in terms of micro-mechanical analyses.Project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China     

空间薄膜结构动态测试研究最新进展

空间薄膜结构是一种主要由薄膜材料制成的新型大型轻量化结构,在深空探测中可用于构建大型天线、太阳帆、太阳能集中器等新概念飞行器。它具有超低频率、密集模态、局部模态、几何大变形、高柔性、低密度、强非线性、以及承载能力随充气压力改变等一系列特点,传统的实验模态分析方法已经不满足此类结构的测试要求。同时在地面测试时容易受空气附加质量、地球重力及温度、湿度环境影响,这给动态测试带来很大困难。本文首先总结了适合薄膜空间结构的动态测试技术如新型智能传感器,激光测量和数字图像测量等非接触测试方法最新进展,并比较分析各测试方法优缺点。此外对微重力、真空、交变温度等空间环境对动态测试结果的影响进行总结,存在缺陷对动态测试结果的影响进行评述,最后针对目前空间薄膜结构动态测试中存在的问题进行探讨并指出未来发展方向。     

Nonlinear Bending Theory of Diagonal Square Pyramid Reticulated Shallow Shells

ＩｎｔｒｏｄｕｃｔｉｏｎＤｏｕｂｌｅ＿ｄｅｃｋｒｅｔｉｃｕｌａｔｅｄｓｈｅｌｌｓａｓａｍａｉｎｆｏｒｍｏｆｌａｒｇｅｓｐａｃｅｓｔｒｕｃｔｕｒｅｓ,ａｒｅｗｉｄｅｌｙｕｓｅｄｉｎｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇａｎｄｍａｎｙｏｔｈｅｒｆｉｅｌｄｓ[1,2 ].Ｏｎｅｏｆｔｈｅｍｉｓｔｈｅｄｉａｇｏｎａｌｓｑｕａｒｅｐｙｒａｍｉｄｒｅｔｉｃｕｌａｔｅｄｓｈａｌｌｏｗｓｈｅｌｌ.Ｔｈｅｓｈｅｌｌｃｏｎｓｉｓｔｓｏｆｒｅｖｅｒｓｅｓｑｕａｒｅｐｙｒａｍｉｄｓｗｈｏｓｅｖｅｒｔｅｘｅｓａｒｅｌｉｎｋｅｄｂｙｌｏ…     

On Constitutive Equations of Cauchy Elastic Solids: All Kinds of Crystals and Quasicrystals

Our concern is with the problem of determining general reduced forms of constitutive equations of Cauchy elastic solids under all kinds of material symmetries, including well-known crystal classes and newly discovered quasicrystal classes. By means of Tschebysheff polynomials we present in unified forms simple irreducible representations for elastic constitutive equations under the infinitely many subgroup classes C _2m+1, C _2m+2, D _2m+1 and D _2m+2 for all m = 1, 2,... Moreover, we provide a simple representation for elastic constitutive equations under the most complicated point group, i.e. the icosahedral group. Each presented representation is expressed in terms of not more than nine polynomial tensor generators only. This revised version was published online in August 2006 with corrections to the Cover Date.     

On Compressible Materials Capable of Sustaining Axisymmetric Shear Deformations. Part 4: Helical Shear of Anisotropic Hyperelastic Materials

Conditions on the form of the strain energy function in order that homogeneous, compressible and isotropic hyperelastic materials may sustain controllable static, axisymmetric anti-plane shear, azimuthal shear, and helical shear deformations of a hollow, circular cylinder have been explored in several recent papers. Here we study conditions on the strain energy function for homogeneous and compressible, anisotropic hyperelastic materials necessary and sufficient to sustain controllable, axisymmetric helical shear deformations of the tube. Similar results for separate axisymmetric anti-plane shear deformations and rotational shear deformations are then obtained from the principal theorem for helical shear deformations. The three theorems are illustrated for general compressible transversely isotropic materials for which the isotropy axis coincides with the cylinder axis. Previously known necessary and sufficient conditions on the strain energy for compressible and isotropic hyperelastic materials in order that the three classes of axisymmetric shear deformations may be possible follow by specialization of the anisotropic case. It is shown that the required monotonicity condition for the isotropic case is much simpler and less restrictive. Restrictions necessary and sufficient for anti-plane and rotational shear deformations to be possible in compressible hyperelastic materials having a helical axis of transverse isotropy that winds at a constant angle around the tube axis are derived. Results for the previous case and for a circular axis of transverse isotropy are included as degenerate helices. All of the conditions derived here have essentially algebraic structure and are easy to apply. The general rules are applied in several examples for specific strain energy functions of compressible and homogeneous transversely isotropic materials having straight, circular, and helical axes of material symmetry.