声子晶体中SH波缺陷模的相干叠加理论

利用波的相干叠加原理推导出一维掺杂声子晶体中SH波缺陷模的透射率公式和频率公式,即建立了缺陷模的相干叠加法。将相干叠加法与转移矩阵法和共振理论进行了比较研究,结果表明缺陷模的相干叠加法具备转移矩阵法和共振理论各自的优点,又克服了转移矩阵法和共振理论各自的不足。相干叠加法是研究一维掺杂声子晶体中SH波缺陷模的一种更有效的方法。     

利用叠加理论研究固-液声子晶体纵波的能带结构

采用相干叠加原理推导出一种研究一维固-液有限周期声子晶体中纵波的透射率公式,建立了一种研究一维固-液有限周期声子晶体能带的新方法——波叠加理论。将波叠加理论和转移矩阵法进行了比较研究,结果表明波叠加理论和转移矩阵法得出的结果是一致的。波叠加理论不仅具有转移矩阵法的优点,而且又克服了转移矩阵法的不足。因此波叠加理论是一种研究一维固-液有限周期声子晶体中纵波能带的更为有效的方法。     

非局部弹性理论概述及在当代材料背景下的一些进展

局部作用原理在发展经典连续介质力学的本构关系中起着重要的作用，由此导出的简单物质理论得到了广泛的应用．然而，随着科技的发展，各种具有微结构的新材料不断涌现，理论和实验表明，非局部理论可以更好地刻画这些材料的宏观力学行为．本文简要介绍了一些传统的非局部弹性理论，包括Eringen 理论、Kunin 理论、Mindlin 理论；阐述了针对复合材料发展的，具有时间-空间非局部特征的Willis 方程、最新的时间-空间耦合非局部弹性动力学理论以及近场动力学理论．时间-空间非局部理论反映了复合材料宏观性能固有的非局部特征，而具有空间非局部特征的近场动力学理论便于处理具有不连续性的问题．最后，本文讨论了非局部理论的发展中值得关注的一些问题.     

Finite expansion of a hole in an elastic-plastic thin plate of finite thickness

A finite deformation theory for axially symmetric thin elastic-plastic plates is obtained by a consistent approximation from the corresponding three-dimensional theory. This theory can be applied to plates of finite thickness, and is different from the usual plane stress theory. The problem of the expansion of a circular hole in an infinite plate is investigated and the effect of the transversely variable stress components is studied.     

基于质量守恒的缆索计算理论与找形解析算法

旨在解决既有缆索计算理论的基本假定不合理问题,基于质量守恒原则推导了精细化缆索计算理论;根据拉格朗日坐标建立了考虑缆索截面变形后受拉刚度变化的改进弹性悬链线计算理论。研究结果表明,精细化缆索计算理论与改进的分段悬链线计算理论具有等价性;自重下跨度为888 m的缆索找形计算案例中,精细化缆索计算理论与悬链线方程理论的缆力及高程差值分别为61.5 kN和-158.7 mm,与弹性悬链线理论计算差值对应分别为1.9 kN和0.5 mm;受外载下跨度为1038 m缆索找形计算案例中,推导的精细化缆索计算理论与悬链线方程理论缆力差值分别为77.8 kN,与弹性悬链线理论无应力长度计算差值控制为1.0 mm。精细化缆索单元计算理论及缆索找形算法可作为缆索承载结构体系一种完备的精细化计算理论与方法。     

Initial planar deformation of dilatant granular materials

A theory for the initial planar deformation of dilatant granular materials based on a kinematic proposal of R. Butterfield and R.M. Harkness (1972) is presented. The theory introduces an additional parameter called the angle of dilatancy into the traditional structure of plasticity theories for granular materials and soils. When the angle of dilatancy is zero, the present theory reduces to the theory introduced by A.J.M. Spencer in 1964. When the angle of dilatancy is equal to the angle of internal friction, the present theory reduces to the planar form of the theory introduced by D. C. Drucker and W. Prager in 1952. The properties of the theory presented here include coincidence of the stress and velocity characteristics, realistic energy dissipation predictions, and, in general, non-coincidence of the principal axes of stress and strain-rate. However, the angle of dilatancy is assumed to be a constant in this analysis and it does not decrease to zero with increased monotonic shearing deformation as experiment requires that it should, the theory therefore being limited to the initial deformation of dilatant granular materials.     

Modified Kirchhoff's theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoff's boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis.     

Generalized theory of multilayer plates

The layer-wise generalized theory of elastodynamic of multilayer plates is presented in this paper. This theory is based on expanding the displacement vector components of each layer into power series about the transverse coordinate. The number of terms retained in the power series is arbitrary and it is chosen depending on the problem being considered and the solution accuracy required. The system of governing equations is obtained by Hamilton's variation principle.The possibilities of the theory proposed and validity of results obtained are illustrated by examples of investigating the strain-stressed state of one- and three-layer structures. The issues of applicability of two-dimensional approximations built on the basis of the power series method are considered with respect to calculation of displacements, inplane and transverse stresses in multilayer plates under dynamic loading. Calculation results are compared with data obtained from Ambartsumyan's theory (the hypothesis of a unique non-strained normal for the pack), the layer-wise theory based on the broken line hypothesis as well as the three-dimensional elasticity theory.     

Theory of nonlocal asymmetric elastic solids

In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum fieM theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic fiteld theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation, We show that there is the nonlocal body moment in the nonlocal elastic solids. The noniocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.     

Continuum theory of dense rigid suspensions

A continuum theory of rigid suspensions is introduced. Balance laws and constitutive equations of micropolar continuum theory are modified and extended for the characterization of dense rigid suspensions. Thermodynamic restrictions are imposed. The general theory is specialized to the case of dense rigid fiber and spherical suspensions. Dilute suspensions in Newtonian fluids are obtained as special cases. Motions of rigid fiber suspensions in viscometric flows are determined as applications of the theory.     

Evolution of the Theory of Laminated Plates and Shells

The theory of laminated plates and shells is considered. Three-dimensional models of layered systems and methods of reducing them to two-dimensional models are elucidated. An analysis is made of how two-dimensional models are constructed by the method of hypotheses. Two basic approaches to the construction are presented: one leads to the discrete structural theory of laminated systems and the other to continuous structural theory. Attention is drawn to transverse shear and reduction in nonclassical theories of high approximation. The finite-element implementation of the theory is described. Examples of analysis by various models are given. Results of an applicability analysis of various theories and experimental data supporting them are presented. New research areas for the theory of laminated structures are pointed out.     

A theory of the adaptive growth of biological materials

Summary In this paper, a new theory of the adaptive growth of biological materials is presented. The theory is derived from the basic laws of continuum mechanics. The material is described as a classical mixture of solid material and fluid. It will be shown that several well-known models of the adaptive growth are embedded in this more general theory. In addition, it is clarified on which material assumptions these models are based. Finally, a solution procedure for the new theory is developed, and several examples are given. Received 31 March 1999; accepted for publication 1 June 1999     

Mathematical Models and Methods of the Mechanics of Stochastic Composites

The basic approaches used in mathematical models and general methods for solution of the equations of the mechanics of stochastic composites are generalized. They can be reduced to the stochastic equations of the theory of elasticity of a structurally inhomogeneous medium, to the equations of the theory of effective elastic moduli, to the equations of the theory of elastic mixtures, or to more general equations of the fourth order. The solution of the stochastic equations of the elastic theory for an arbitrary domain involves substantial mathematical difficulties and may be implemented only rather approximately. The construction of the equations of the theory of effective moduli is associated with the problem on the effective moduli of a stochastically inhomogeneous medium, which can be solved by the perturbation method, by the method of moments, or by the method of conditional moments. The latter method is most appropriate. It permits one to determine the effective moduli in a two-point approximation and nonlinear deformation properties. In the structure of equations, the theory of elastic mixtures is more general than the theory of effective moduli; however, since the state equations have not been strictly substantiated and the constants have not been correctly determined, theoretically or experimentally, this theory cannot be used for systematic designing composite structures. A new model of the nonuniform deformation of composites is more promising. It is constructed by performing strict mathematical transformations and averaging the output stochastic equations, all the constants being determined. In the zero approximation, the equations of the theory of effective moduli follow from this model, and, in the first approximation, fourth-order equations, which are more general than those of the theory of mixtures, follow from it     

A note on a new theory of turbulence

In this paper,the creation and annihilaton of turbulent eddies are described aselementary particles in the quantum field theory.An elementary particle may be consideredas a solid entity as it exists in quantum theory,but a turbulent eddy is often changed in sizeand shape with time due to its energy dissipation in a turbulent field.Therefore,in order toapply the method of the quantum field theory to the turbulent field by analogy,the entity ofthe same eddy should be defined firstly.According to the linearized theory,the turbulenteddies with the similarity character in lime duration may be considered as the entity of thesame eddy,and the creation and annihilation of turbulent eddies without the similarcharacters are related to the interaction term φ_2 in equation(2.6).Then,the creationoperator and annihilation operator similar to those in the quantum field theory are used todescribe the state of turbulent eddy field.Finally,a“Schrǒdinger”equation of turbulenteddies is formulated based upon the nonline     

连续系统的界带分析方法

基于分析结构力学提出的界带分析方法,将子结构间的分界面延拓为有一定宽度的分界带/分界域,从而可以用于分析计算结构的非局部效应。界带分析方法首先在离散结构的分析计算中取得了成功,从而验证了该套理论算法的准确性。离散结构按界带宽度（影响域范围）划分子结构,因而限制了子结构区段积分计算的最小步长;而连续系统则要求可以实现任意步长的积分运算。通过引入步进的计算方法,界带分析方法可以实现任意步长的积分计算,进而可以解决连续系统的积分问题。通过数值算例验证了连续系统的界带分析方法的准确性和可行性,也为进一步研究该套计算方法在分析动力学中的应用打下基础。     

Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

In this paper, the stability and bifurcation analysis of symmetrical and asymmetrical micro-rotating shafts are investigated when the rotational speed is in the vicinity of the critical speed. With the help of Hamilton’s principle, nonlinear equations of motion are derived based on non-classical theories such as the strain gradient theory. In the dynamic modeling, the geometric nonlinearities due to strains, and strain gradients are considered. The bifurcations and steady state solution are compared between the classical theory and the non-classical theories. It is observed that using a non-classical theory has considerable effect in the steady-state response and bifurcations of the system. As a result, under the classical theory, the symmetrical shaft becomes completely stable in the least damping coefficient, while the asymmetrical shaft becomes completely stable in the highest damping coefficient. Under the modified strain gradient theory, the symmetrical shaft becomes completely stable in the least total eccentricity, and under the classical theory the asymmetrical shaft becomes completely stable in the highest total eccentricity. Also, it is shown that by increasing the ratio of the radius of gyration per length scale parameter, the results of the non-classical theory approach those of the classical theory.     

新型整体-局部高阶剪切变形理论及层合板精化三角形单元

基于整体-局部位移方法,建立了一种高阶剪切变形理论。整体位移部分采用的是Reddy理论的位移模式（1984）,局部位移为LIXY等（1997）建立的1,2-3理论的局部函数。这一理论使满足自由表面条件的Red@理论进一步满足层间位移、应力连续,同时有效减少了1,2—3理论的未知数个数。基于此理论深入开展了有限元法研究,建立了满足C^1连续条件的精化三节点三角形单元（每个节点参数为9个）。计算结果表明：建立的精化单元能准确计算整体位移和层间应力。     

THEORY OF ELASTICITY OF AN ANISOTROPIC BODY FOR THE BENDING OF BEAMS

A theory of elasticity for the bending of orthogonal anisotropic beams has been developed by analogy with the special case, which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two deminsions. In this paper, we present a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger. It is pointed out that Reissner's theory to account for the effect of transverse shear deformation is not very approximate in the components of stress,     

Towards an acoustoelastic theory for measurement of residual stress

The rudiments of an acoustoelastic theory is developed within the framework of linear elasticity with initial stress. Since no assumption is made about the origin of the initial stress, our acoustoelastic theory will be applicable to evaluation of stress in plastically deformed bodies, provided that the superimposed ultrasonic waves be hyperelastic. New universal relations are deduced. An approach to evaluation of stress which does not use calibration specimens and makes full use of universal relations in our acoustoelastic theory is advocated. Examples are given which illustrate application of our theory to evaluate residual stress in plates. Preliminary corroborations of our theory are provided by the recent experiments of King & Fortunko and Thompson et al.