Two photoviscoelasticity experiments using analog data reduction

A tensile analog may conveniently be used to determine the history of the principal-stress difference from the results of some photoviscoelastic model tests. With this method, the model test is run, and the fringe-order history at the point (s) of interest in the model is recorded. A tensile specimen of the same material is placed in a loading frame and loaded with a stress history which forces it through the fringe-order history observed in the model. This stress history is then the desired principal-stress-difference history occurring in the model. The stress history at points in two nonhomogeneous models was determined with a tensile analog. The uses and limitations of the analog technique are discussed.     

Linear Potentials in Nonlinear Potential Theory

Pointwise gradient bounds via Riesz potentials, such as those available for the linear Poisson equation, actually hold for general quasilinear degenerate equations of p-Laplacean type. The regularity theory of such equations completely reduces to that of the classical Poisson equation up to the C ¹-level.     

Theory of electromagnetic flow measurement

A study is made of the influence of an inhoinogeneous profile of the concentration of red blood corpuscles on the sensitivity of an electromagnetic flowmeter under conditions of a pulsating flow. The part played by microscopic correlations and the applicability of the single-velocity approximation in the averaged Ohm's law are examined. On the basis of the solution of an electro-dynamic boundary-value problem, an expression is obtained for the flowmeter sensitivity for arbitrary axisymmetric velocity profile and different conduct'ivities of the core of the flow, the wall layer, and the wall. The solution to the problem of Viscous flow under the influence of an oscillating pressure gradient [8] is generalized to the case of a two-layer distribution of the viscosity. It is shown that the presence of a wall layer of pure plasma leads to a phase shift between the oscillations of the electric intensity and the volume flow rate of the suspension. If the amplitude of the oscillations in the flow rate is comparable with the constant component, the instantaneous sensitivity of the flowmeter changes rapidly with the time and the characteristic of the instrument becomes essentially nonlinear.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 114–119, May–June, 1981.I am grateful to S. A. Regirer for a helpful discussion of the work.     

各向异性非线性固体力学的规范空间理论

本文在弹性规范空间概念基础上，利用非平衡态热力学理论，证明了各向异性固体力学非线性问题规范空间场以及不可逆过程本征解的存在。损伤对结构刚度的弱化效应和损伤诱发各向异性效应分别反映在本征弹性和相应的模态向量中。在简正坐标中考察各向异性体变形时，材料的行为以六个普通的粘弹性Ｍａｘｗｅｌｌ方程描述，总的响应由模态叠加得到。以此为基础给出的非线性本构方程具有坐标转换不变性，最后给出了二个具体的算例。     

Nonlinear Boundary Conditions in Kirchhoff-Love Plate Theory

Most of the derivations of the mechanical behavior of a plate as the limit behavior of a three-dimensional solid whose thickness tends to zero deal with stationary homogeneous linear boundary conditions on the lateral boundary. Here, in the framework of small strains, we rigorously determine a large class of steady-state or transient nonlinear boundary conditions which provide asymptotic kinematics of Kirchhoff-Love type.      

Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.     

Nonlinear Dynamics of Shells: Theory,Finite Element Formulation,and Integration Schemes

The paper is concerned with a dynamical formulation of a recently established shell theory capable to catch finite deformations and falls within the class of geometrically exact shell theories. A basic aspect is the design of time integration schemes which preserve specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the applied forces allow to. The integration method differs from the one recently proposed by Simo and Tarnow in being applicable without modifications to shell formulations with linear as well as nonlinear configuration spaces and in being independent of the nonlinearities involved in the strain-displacement relations. A finite element formulation is presented and various examples of nonlinear shell dynamics including large overall and chaotic motions are considered.     

Applications of Nonlinear Dynamical Systems Theory in Developmental Psychology: Motor and Cognitive Development

Applications of nonlinear dynamical systems theory to psychology have led to recent advances in understanding neuromotor development and advances in theories of cognitive development. This article reviews published findings associated with a specific coherent and influential application from which a theory of adaptive, self-organized cognition has been derived and related to a theory of developmental dynamics of the neuromotor system. The review focuses on implications of the two theories for quantifying developmental phenomena, and suggests a method for quantifying the cognitive theory.     

一种基于Gauss von Mises分布模型的非线性量测更新方法

基于状态空间模型的许多传统滤波算法都基于Rn空间中的高斯分布模型,但当状态向量中包含角变量或方向变量时,难以达到理想的效果。针对J.T.Horwood等提出的nS?R流形上的Gauss Von Mises(GVM)多变量概率密度分布,扩展了狄拉克混合逼近方法,给出了联合分布的GVM逼近方法,推导了后验分布的GVM参数计算公式,设计了量测更新状态估计算法。将J.T.Horwood等的时间更新算法与所提出的量测更新算法相结合,可实现基于GVM分布的递推贝叶斯滤波器(GVMF)。仿真结果表明,当状态向量符合GVM概率分布模型时,GVMF对角变量的估计明显优于传统的扩展卡尔曼滤波器。     

A Simple Nonlinear Thermodynamic Theory of Arbitrary Elastic Beams

A ‘classical’ theory of beams (i.e., a theory in which the basic kinetic variables are a stress resultant and a stress couple) undergoing elastic, thermodynamic processes is developed by first deriving exact beamlike (one-dimensional) equations of motion and a beamlike Second Law (Clausius–Duhem inequality) by descent from three-dimensions. Then what may be considered as the three basic assumptions of a classical theory are introduced: an assumed form of the First Law (conservation of energy), a relaxed form of the Second Law, and a general form of the constitutive relations. Throughout, detailed specification of geometry, kinematics, or constitution is minimized. It is shown how the kinematic Kirchhoff hypothesis may be avoided by first introducing a mixed-energy density and then imposing a logically more satisfying constitutive Kirchhoff hypothesis. Mathematics Subject Classifications (2000) 74A15, 74B20, 74K10     

On the Nonlinear Theory of Thermoviscoelastic Materials with Voids

Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By emphasizing the geometric nature of such anomalies we seek their representations for materially uniform crystalline elastic solids. In particular, we introduce a quasi-plastic deformation framework where the multiplicative decomposition of the total deformation gradient into an elastic and a plastic deformation is established such that the plastic deformation is further decomposed multiplicatively in terms of a deformation due to dislocations and another due to metric anomalies. We discuss our work in the context of quasi-plastic strain formulation and Weyl geometry. We also derive a general form of metric anomalies which yield a zero stress field in the absence of other inhomogeneities and any external sources of stress.     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton–Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading.

     

Linear and Nonlinear Aerodynamic Theory of Interaction between Flexible Long Structure and Wind

ＩｎｔｒｏｄｕｃｔｉｏｎＡｌｏｎｇｗｉｔｈｔｈｅｉｎｃｒｅａｓｅｏｆｔｈｅｆｌｅｘｉｂｉｌｉｔｙｏｆｓｌｅｎｄｅｒｓｔｒｕｃｔｕｒｅｓｅｔｉｎｔｈｅｗｉｎｄｆｉｅｌｄ ,ｓｕｃｈａｓｔｈｅｌｏｎｇ＿ｓｐａｎｂｒｉｄｇｅａｎｄｈｉｇｈ＿ｒｉｓｅｂｕｉｌｄｉｎｇ ,ｔｈｅａｃｔｉｏｎｓｏｆｕｎｓｔｅａｄｙａｅｒｏｄｙｎａｍｉｃｆｏｒｃｅｓｗｉｌｌａｃ ｃｅｌｅｒａｔｅ,ａｎｄｈｏｗｔｏｓｏｌｖｅｔｈｅａｅｒｏｅｌａｓｔｉｃｐｒｏｂｌｅｍｓｉｓｇｅｔｔｉｎｇｍｏｒｅｉｍｐｏｒｔａｎｔ.Ｔｈｅａｅｒｏｅｌａｓ…     

Nonlinear Theory of Dynamic Stability for Laminated Composite Cylindrical Shells

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎｃｏｍｐｏｓｉｔｅｃｙｌｉｎｄｒｉｃａｌｓｈｅｌｌｓａｒｅｕｎｄｅｒｔｈｅａｃｔｉｏｎｏｆｄｙｎａｍｉｃｌｏａｄｉｎｇ ,ｔｈｅｙｍａｙｆａｌｌｉｎｄｙｎａｍｉｃｂｕｃｋｌｉｎｇｏｒｄｙｎａｍｉｃｉｎｓｔａｂｉｌｉｔｙ .Ｉｆｔｈｅｄｙｎａｍｉｃｌｏａｄｉｓｓｕｄｄｅｎｌｙａｐｐｌｉｅｄ ,ｏｒｉｔｉｓｃｈａｎｇｉｎｇｉｎｓｔａｎｔａｎｅｏｕｓｌｙ ,ｓｕｃｈａｓｉｍｐｕｌｓｉｖｅｌｏａｄｉｎｇ ,ｔｈｅｎ ,ｄｙｎａｍｉｃｂｕｃｋｌｉｎｇｗｉｌｌｈａｐｐｅｎｆｏｒｔｈｅｓｈ…     

Nonlinear Bending Theory of Diagonal Square Pyramid Reticulated Shallow Shells

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

Existence Theory by Front Tracking for General Nonlinear Hyperbolic Systems

We consider the Cauchy problem for a strictly hyperbolic, N × N quasilinear system in one-space dimension