Asymptotic theory for static behavior of elastic anisotropic I-beams

End effects for prismatic anisotropic beams with thin-walled, open cross-sections are analyzed by the variational-asymptotic method. The decay rates for disturbances at the ends of prismatic beams are evaluated, and the most influential end disturbances are incorporated into a refined beam theory. Thus, the foundations of Vlasovs theory, as well as restrictions on its applicability, are obtained from the variational-asymptotic point of view. Vlasovs theory is proved to be asymptotically correct for isotropic I-beams. The asymptotically correct generalization of Vlasovs theory for static behavior of anisotropic beams is presented. In light of this development, various published generalizations of Vlasovs theory for thin-walled anisotropic beams are discussed. Comparisons with a numerical 3-D analysis are provided, showing that the present approach gives the closest agreement of all published theories. The procedure can be applied to any thin-walled beam with open cross-sections.     

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.     

弹性体表面分层压缩失稳问题的数学弹性力学解

采用数学弹性力学的稳定平衡方程并结合富氏积分变换的方法研究了含表面平行裂纹的弹性体在压缩载荷下的表面分层失稳问题。导出了一级显式的精确齐次奇异积分方程组,然后.通过Gauss-Chebyshev积分公式,得到一组齐次代数方程组,从而求出临界压缩载荷。并将结果与经典的材料力学梁板稳定的研究方法所得结果进行了比较,指出经典方法误差太大而不适于求解此问题。最后,利用数学弹性力学解求出的等效弹性支承常数给出一个简单精确的临界压缩载荷计算公式。     

Macro slip theory of plasticity for polycrystalline solids

A macro slip theory is presented in this paper. Four independent slip systems are proposed for polycrystalline solids. Each slip system consists of a slip plane which lies on a face of the octahedron in stress space and a slip direction which is coincident with shear stress acting on the same face of the octahedron. It is proved that for proportional loading, present results are identical with the classical flow theory of plasticity. For nonproportional loading, the macro slip theory shows good predicting ability. The calculated results are in good agreement with the experimental data. The project supported by Chinese Academy of Science     

Viscoplasticity theory based on overstress. The prediction of monotonic and cyclic proportional and nonproportional loading paths of an aluminum alloy

An isotropic formulation of the viscoplasticity theory for small strain and based on overstress with a differential growth law for the equilibrium stress is introduced. The four material constants and the two material functions of the theory are determined from uniaxial tensile tests involving strain-rate changes at room temperature and performed on a 6061 T6 Aluminum Alloy. Subsequently the theory is used to predict the biaxial behavior under axialtorsion loading. All tests are under strain control and involve proportional loading and axial followed by torsional straining (and vice versa). Cyclic histories include in-phase and out-of-phase cycling. The predictions of the theory are very reasonable for this cyclically neutral alloy. For cyclic hardening or softening materials a modification of the theory is necessary and is under development.     

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。     

From Double Bind to N-Bind: Toward a New Theory of Schizophrenia and Family Interaction

Double Bind Theory has long been discredited as a viable theoretical framework to understand the relationship between schizophrenia and family interaction. Since research continues to indicate that the family environment plays a crucial role in the development and/or maintenance of the disorder, a reconsideration of the status of Double Bind is both necessary and timely. This paper utilizes a Nonlinear Dynamical Systems framework to bring the theory up to date with current dynamical thinking, and renames the resulting model N-Bind theory. The premises of N-Bind theory are discussed, and the symptoms of schizophrenia are described in light of the theory. The compatibility of N-Bind theory with the Vulnerability-Stress model is discussed, and a procedure is proposed to test the two hypotheses which postulate on different levels of analysis that Binds are more likely to occur in families with than without a schizophrenic member. Some of the implications for treatment and prevention are considered, should the theory be supported by empirical evidence.     

Initiation of localized shear bands in plane strain

This study is concerned with the initiation of localized shear bands in plane-strain tension and compression. A theoretical framework which views the initiation of such shear bands as a bifurcation phenomenon from a homogeneous equilibrium field in an elastic-plastic body is first briefly reviewed, and then the predictions of the theory are compared with some experimental observations on an aged maraging steel. The experiments support the physical relevance of the theory within the framework of continuum mechanics.Specifically, the comparison between theory and experiment is concerned with the critical strains to localization and the orientation of the shear bands relative to the load axis. The theoretical predictions are only in qualitative agreement with the experimental observations. A better agreement is obtained with use of the constitutive equations corresponding to the classical deformation theory (a simple vertex model) than with use of the constitutive equations of the classical flow theory. It is concluded that better constitutive equations for elastic-plastic materials are needed before theoretical predictions can be obtained which might be expected to be in closer quantitative accord with experiment.     

Theory of multiphase mixtures—A thermomechanical formulation

The paper presents a theory of mixtures with the nonzero interfacial area between the constituents of the mixture. The conservation laws are physically motivated by utilizing a volume averaging procedure and by the definition of a mapping transformation. It is shown that the theory constructed in this manner is consistent with the theory of mixtures with a vanishingly small interfacial area and that a second law of thermodynamics can be assigned for each phase of the mixture. The conservation laws are examined for invariance properties with the principle of the material frame indifference, and a particular constitutive assumption is discussed. Also presented in the paper are the conservation laws in the integral form and the jump conditions for the singular surfaces in the multiphase mixture.     

A continuum theory of elastic material surfaces

A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended.     

压电复合材料层板柱面弯曲的精化理论

本研究旨在建立精确的压电复合材料层板理论。位移场和电势场采用近似表达，其沿板厚的分布通过构造高精度的位移分布函数和电势分布函数来描述。这两个函数由三雏弹性平衡方程和静电平衡方程的特解来导出，从而满足复杂的力电耦合关系和各类连续条件，保证了本文理论的高精度。本文理论仅涉及4个位移和电势变量，且不随层数的增加而增多，较之变量随层数而增多的分层理论简单得多，平衡方程形式简单；也便于发展成有限元等数值模型。通过与三维精确解比较，算例显示了本文理论的高精度和有效性。     

Nonisothermal flow of polymer melts

The Curtiss-Bird theory for polymer melts is modified to allow the temperature to be a function of time. The resulting constitutive equation involves integrals over the temperature history of the polymer. The predictions of this constitutive equation for the inception of uniaxial elongation with simultaneous cooling at a constant rate are calculated and compared with the experimental data of Matsumoto and Bogue. Qualitative agreement between the theory and the data is obtained when the link tension coefficient in the Curtiss-Bird theory is not equal to zero, but such agreement cannot be obtained when this coefficient is equal to zero. The extension of the theory to include spatially varying temperature is also discussed.     

高维非线性系统的全局分岔和混沌动力学研究

综述了Melnikov方法的发展历史, 从1963年苏联学者Melnikov提出该方法开始, 一直到目前广义Melnikov方法的提出和发展. Melnikov方法的发展历程可以概括为3 个阶段, 分别综述了每一个阶段Melnikov方法的扩展和应用, 论述了国内外在该方向的研究现状和所获得的主要结果, 指出了各种Melnikov方法之间的联系、存在的问题和不足. 为了对比两种研究高维非线性系统多脉冲混沌动力学的理论, 本文综述了另外一种全局摄动理论, 即能量相位法, 总结了该方法十几年来的发展历史以及国内外的理论研究成果和工程应用实例, 阐述了能量相位法发展的根源以及与Melnikov方法的内在联系, 比较了能量相位法和广义Melnikov方法两种理论研究对象的差别, 以及各自所存在的不足和问题. 简要论述了能量相位法和广义Melnikov方法的理论体系, 并利用广义Melnikov方法分析了四边简支矩形薄板的多脉冲混沌动力学, 数值模拟进一步验证了理论研究的结果. 最后, 详细综述了两种理论的缺点和不足, 说明今后全局摄动理论的发展方向.     

A properly invariant theory of small deformations superposed on large deformations of an elastic rod

In the context of the direct or Cosserat theory of rods developed by Green, Naghdi and several of their co-workers, this paper is concerned with the development of a theory of small deformations which are superposed on large deformations. The resulting theory is properly invariant under all superposed rigid body motions. Furthermore, it is also valid for elastic rods which are subject to kinematical constraints, and it specializes to a linear theory of an elastic rod which is invariant under superposed rigid body motions. The construction of these theories is based on the method developed by Casey & Naghdi [1] who established similar theories for unconstrained nonpolar elastic bodies.     

A micropolar mixture theory of multi-component porous media

A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen＇s model.     

考虑材料拉压异性的固支圆板塑性极统一解

本文采用最新的统一强度理论求出了固支圆板的塑性极限荷载,内力场及速度的统一解;得出了强度理论参数b及材料的不同拉压比α对塑性极限的影响曲线,所给出的解可以灵活地适用于各种不同特性的材料及机械、土木、航空等工程的相关结构中,文献中已有的Tresca解,Mises解和双剪统一屈服准则解均为本文的特例,本文的统一解还给出了一系列新的结果,统一解大于Tresca,Mohr-Coulomb的单剪理论解,它可以更好地发挥材料的强度潜力,工程应用可以取得明显的经济效益。     

Timoshenko-Type Theory in the Stability Analysis of Corrugated Cylindrical Shells

A technique is proposed for stability analysis of longitudinally corrugated shells under axial compression. The technique employs the equations of the Timoshenko-type nonlinear theory of shells. The geometrical parameters of shells are specified on discrete set of points and are approximated by segments of Fourier series. Infinite systems of homogeneous algebraic equations are derived from a variational equation written in displacements to determine the critical loads and buckling modes. Specific types of corrugated isotropic metal and fiberglass shells are considered. The calculated results are compared with those obtained within the framework of the classical theory of shells. It is shown that the Timoshenko-type theory extends significantly the possibility of exact allowance for the geometrical parameters and material properties of corrugated shells compared with Kirchhoff–Love theory.     

Buckling analysis of cylindrical thin-shells using strain gradient elasticity theory

The stability problem of cylindrical shells is addressed using higher-order continuum theories in a generalized framework. The length-scale effect which becomes prominent at microscale can be included in the continuum theory using gradient-based nonlocal theories such as the strain gradient elasticity theories. In this work, expressions for critical buckling stress under uniaxial compression are derived using an energy approach. The results are compared with the classical continuum theory, which can be obtained by setting the length-scale parameters to zero. A special case is obtained by setting two length scale parameters to zero. Thus, it is shown that both the couple stress theory and classical continuum theory forms a special case of the strain gradient theory. The effect of various parameters such as the shell-radius, shell-length, and length-scale parameters on the buckling stress are investigated. The dimensions and constants corresponding to that of a carbon nanotube, where the length-scale effect becomes prominent, is considered for this investigation.     

Bending behavior of a rectangular plate with a bitrapezoidal cross section

A theory is developed for the transverse deflections when a rectangular plate having a bitrapezoidal cross section is subjected to a uniform longitudinal curvature. The theoretical solutions are compared with earlier results presented by Lamb and Fung and Wittrick. Experimental results are compared with the theory and good agreement is obtained over the range of curvatures tested.