基于悬链线理论的海带打结原理研究

机械化海带打结是当今未解决的技术难题,目前研制的海带打结机难以达到产业化要求的99%的打结成功率. 为了研究海带打结机的海带成结原理并提高海带打结成功率,利用悬链线理论对海带打结过程进行了分析. 建立了海带线的悬链线数学模型,提出了端点等高、端点不等高和受到端点外其他约束等各种悬链线方程的解法,分析了海带线打结过程中4个不同阶段所处的状态,通过将海带线在4种状态下的空间曲线向指定平面投影的方法研究了打结原理,结果表明海带线符合扭转打结法的条件,证明了此种海带打结方法的正确性和可行性,为提高海带打结机打结成功率提供了理论上的指导.     

A gradient thermodynamic theory of self-organization

Summary In this paper we present a gradient theory of internal variables in a thermodynamic context of the Gibbs free energy density ø. A fundamental point of the theory is that ø is a function of three different classes of internal variables: (a) tensorial dissipative and local; (b) vectorial dissipative and non-local and (c) vectorialinviscid and non-local. These classes obey different types of evolution equations. The ones pertaining to the non-local variables are partial differential equations of the diffusion-reaction type. We associate the inviscid non-local variables with energy release mechanisms and show that they lead to patterned deformation, otherwise known as self-organization. We conclude by giving a solution to the problem of a flat plate in nominal axial tension and derive various types of deformation patterns that result from small but unavoidable experimental deviations from this loading.     

A finite element formulation based on Nadai's deformation theory for elasto-plastic analysis

A numerical method of the Newton-Raphson type is presented for elasto-plastic analysis using the finite element method. The method is developed from Nadai's deformation theory and Hooke's law. Numerical examples are used to show that the method provides very rapid solution convergence.     

A thermodynamic approach to the influence of plastic deformation on crack instability

It is argued that the role of plastic deformation in crack growth has been widely misinterpreted. In particular the notion that the work of plastic deformation contributes to the energy balance in such a way as to give rise to an increased effective surface energy is shown to be physically incorrect. A fundamental reappraisal of the role of plastic deformation on the instability of cracks is undertaken and a thermodynamic formulation of the problem of the energetics of crack extension is developed. This is capable of treating both moving cracks and the dislocations producing plastic deformation in a unified manner and provides a powerful tool for the study of combined crack extension and plastic deformation. A rigorous definition of plastic work is also given and it is shown that the crack extension force is the only physically meaningful parameter which can be used in the formulation of a crack instability criterion. The work of plastic deformation is not a part of the crack extension force and should not be included in the criterion for crack instability. It is found that one of the important effects of plastic deformation on crack instability is the shielding effect or the reduction it causes in the magnitude of the stress at the crack tip resulting in a smaller crack extension force. Other possible effects of plastic deformation on crack propagation are briefly discussed.     

A viscoplastic theory with thermodynamic considerations

Summary A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three, fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.     

Discontinuous deformation analysis handling vertex-vertex contact based on principle of least effort

This study establishes an innovative discontinuous deformation analysis by solving the problem of frictional and cohesive contact using an implicit cone complementary formulation. In order to handle singularity associated with the vertex-vertex contact, resistances to motion trend are firstly estimated by introducing the concepts of total and partial contact forces. Based on principle of least effort, the vertex-vertex contact can be converted to a corresponding vertex-edge contact properly. In addition, unnecessary vertex-vertex contacts can be identified. The numerical scheme fully exploits geometric and dynamic conditions of the polygonal block system. As a result, determination of motion trend in the block system is penalty-free without being affected by the time step. The advantages and application prospects of the presented dynamic framework are demonstrated by using several benchmark examples.     

Mesh deformation using the biharmonic operator

The use of the biharmonic operator for deforming a mesh in an arbitrary–Lagrangian–Eulerian simulation is investigated. The biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh. This allows both the position and the normal mesh spacing along a boundary to be controlled, which is important for two‐fluid interfaces and periodic boundaries. At these boundaries, we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary. In addition, results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second‐order partial differential equations. A final advantage is that with the biharmonic operator, the integrity of a grid in a moving boundary layer can be preserved as the boundary moves. The main disadvantage of the approach is its increased computational expense. Copyright © 2003 John Wiley & Sons, Ltd.     

A non-classical third-order shear deformation plate model based on a modified couple stress theory

A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.     

On the thermodynamic theory of mixtures

The present paper presents an axiomatic theory of mixtures which shows that a number of assumptions usually accepted in these theories are not necessary. Using an average method for passing from the microscopic level to the macroscopic one, it is deduced the system of equations of balance and the entropy inequality. The restriction imposed on the constitutive equations by the Clausius-Duhem inequality are studied.     

A new sliding scale principle and the spectroscopic ADC based on this principle

A new sliding scale averaging scheme is proposed. For a N-bit ADC the number of bits M for a sliding scale may be increased up to N−2. At the same time the full number of channels can be used, which is impossible for the conventional sliding scale method. Experiments have been carried out to verify the principle.     

A variational principle motivated by the optimal rod theory

Summary In this work we show that a number of well known nonlinear second order ODE appearing in theoretical physics provide the necessary condition for the minimum of the functional with the Lagrangian . Also we prove that those second-order differential equations may be viewied as conservation laws for the corresponding Euler-Lagrange equations that are the fourth-order ODE. Several special cases that have importance in physics, mechanics and optimal rod theory are studied in detail.     

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddys third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu–Hill equations from which the boundary points on the unstable regions are determined by Bolotins method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.This work was fully supported by grants from the Australian Research Council (A00104534) and from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01 E). The authors are grateful for this financial support.     

Flexural analysis of laminated plates based on trigonometric layerwise shear deformation theory

ABSTRACT

A trigonometric layerwise shear deformation theory is developed for the flexural analysis of laminated plates. The present theory achieves in-plane displacement continuity, transverse shear stress continuity, and traction-free boundary condition. Hence, botheration of shear correction coefficient is neglected. The governing differential equation and boundary conditions are obtained from the principle of virtual work. Although the present analytical method is bounded to a corner supported boundary condition, it neglects the numerical and computational error. Like first-order shear deformation theory, the present theory possesses five numbers of unknowns. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.     

Extrema on thermodynamic properties in Eliashberg theory

We have calculated bounds on thermodynamic properties that apply to any superconductor which can be described by the isotropic Eliashberg equations. The boson exchange mechanism giving rise to the attractive kernel is not specified and its size and shape are varied arbitrarily. We consider the critical field deviation function and the dimensionless ratio T _c ² /H _c ² (0), where is the Sommerfeld constant,T _c is the critical temperature, andH _c (0) is the zero-temperature critical magnetic field. A maximum is also established forH _c (0).     

A refined beam theory based on the refined plate theory

Summary Based on the refined plate theory, a refined theory of rectangular beams is derived by using the Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. The solutions based on the new theory are the same as the exact solutions of elasticity theory. In three examples it is shown that the new theory provides as good or better results than Levinson’s beam theory when compared to those obtained from the linear theory of elasticity.     

Bending of a bimodulus laminated plate based on a higher-order shear deformation theory

This paper presents an exact flexural analysis of rectangular simply supported single-layer and two-layer cross-ply plates of bimodulus materials. The governing equations of a bimodulus plate based on a higherorder shear deformation theory are simplified from the composite plate. The present analysis of displacements in flexure is compared with Bert's results and Turvey's results which are based on Mindlin plate theory. The in-plane stress and bending stress are included in the present study. All the present numerical results are compared with the Mindlin plate theory (first-order plate theory) results. From those comparisons, the effects of higher-order shear deformation terms on the neutral surface locations and the flexure displacements can be observed.