A method for calculating the stress–strain state in the general boundary-value problem of metal forming—part 1

To simulate metal-forming processes, one has to calculate the stress–strain state of the metal, i.e. to solve the relevant boundary-value problems. Progress in the theory of plasticity in that respect is well known, for example, via the slip-line method, the finite element method, etc.) , yet many unsolved problems remain. It is well known that the slip-line method is scanty. In our opinion the finite element method has an essential drawback. (No one is against the idea of the discretization of the body being deformed and the approximation of the fields of mechanical variables.) The results of calculation of the stress state by the FEM do not satisfy Newtonian mechanics equations (these equations are said to be softened, i.e, satisfied approximately) and stress fields can be considered poor for solution of the subsequent fracture problem. We believe that it is preferable to construct an approximate solution by the FEM and soften the constitutive relations (not Newtonian mechanics equations) , especially as, in any event, they describe the rheology of actual deformable materials only approximately. We seem to have succeeded in finding the solution technique.Here we present some new results for solving rather general boundary-value problems which can be characterized by the following: the anisotropy of the materials handled; the heredity of their properties and compressibility; finite deformations; non-isothermal flow; rapid flow, with inertial forces; a non-stationary state; movable boundaries; alternating and non-classical boundary conditions, etc.Solution by the method proposed can be made in two stages: (1) integration in space with fixed time, with an accuracy in respect of some parameters; (2) integration in time of certain ordinary differential equations for these parameters.In the first stage the method is based on the principle of virtual velocities and stresses. It is proved that a solution does exist and that it is the only possible one. The approximate solution softens (approximately satisfies) the constitutive relations, all the rest of the equations of mechanics being satisfied precisely. The method is illustrated by some test examples.     

FSI research in pipeline systems – A review of the literature

This paper provides a broad overview of the literature pertaining to the dynamic analysis of fluid-filled pipe systems considering fluid–structure interaction (FSI). Various types of models and simulation algorithms of different levels of sophistication are compared and their application range discussed. The effects of fluid parameters, structural properties, fluid–structure couplings and boundary conditions on the inherent and dynamic character of pipes conveying fluid are comprehensively compared and contrasted.     

Resonant dynamics in a rotordynamic system with nonlinear inertial coupling and shaft anisotropy

The response of a nonlinear, damped Jeffcott rotor with anisotropic stiffness is considered in the presence of an imbalance. For sufficiently small external torque or large imbalance, resonance capture or rotordynamic stall can occur, whereby the rotational velocity of the shaft is unable to increase beyond the fundamental resonance between the rotational and translational motion. This phenomena provides a mechanism for energy transfer from the rotational to the translational mode. Using the method of averaging a reduced-order model is developed, valid near the resonance, that describes this resonant behavior. The equilibrium points of these averaged equations, which correspond to stationary solutions of the original equations and rotordynamic stall, are described as the applied torque, damping, and anisotropy vary. As the anisotropy increases, assumed to arise from increasing shaft cracks, the torque required to eliminate the possibility of stall increases. However, when the system is started with zero initial conditions, the minimum torque required to pass through the resonance is approximately constant as the anisotropy increases. The predictions from the reduced-order model are verified against numerical simulations of the original equations of motion.     

Three-ion model of EHD flows in the “wire-over-plane” electrode system

The results of numerical simulation of the complete system of electrohydrodynamic equations are presented for a dielectric liquid containing three kinds of ions, namely, two kinds arising owing to impurity molecule dissociation and the third kind arising owing to appearance of ions from liquid molecules with the electron-donor properties in near-electrode reactions. An analysis of the simulation results shows that a small jet of injected ions rapidly recombines with counterions under the conditions of weak injection; therefore, the jet of space charge differs significantly from the injected ion jet. This difference disappears under the conditions of strong injection. The flow structure is in the close correspondence with the results revealed experimentally.     

The onset of convection in the Rayleigh-Bénard problem for compressible fluids

Received August 14, 2000 / Published online January 23, 2001     

Global nonlinear stability in the Bénard problem for a mixture near the bifurcation point

The nonlinear stability of the motionless state of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme, for stress-free and rigid-rigid boundary conditions and Schmidt numbers P_C greater than Prandtl numbers P_T, is studied in the region around the bifurcation point of linear instability. An improvement of the results in Mulone [11] is found for small values of p = P _C /P _T and P_T. For p sufficiently large the critical nonlinear Rayleigh number is very close to the linear one (with relative difference less than in the sea water case) Received December 12, 2002 / Published online April 23, 2003 RID="a" ID="a" e-mail: mbasurto@dmi.unict.it RID="b" ID="b" e-mail: lombardo@dmi.unict.it ID="Communicated by Brian Straugham, Durham"     

On the evolutions of the discontinuities of orders ⩾ m in solutions for quasi-linear systems of PDEs of order m,or for the linearizations of these systems

Summary One considers a system L[u]=0 of PDEs, quasi-linear (according to [1]) and of order m, which possesses a bicharacteristic line , as it happens in the hyperbolic case. For v=0, , –m (>0) let u(^v) be a discontinuity wave of order m+v that solves the system above and whose discontinuity hypersurface includes . The corresponding transport equations along are considered. Furthermore some interesting cases are pointed out, in which these equations turn out to be mutually equivalent in a suitable sense. Some theorems are stated to compare the transport equations for the discontinuities of the above kinds, that are connected with the systems d^hL[u]/dt^h=0 (h=0, , –m) and/or the linearization of the system L[u]=0 around any regular solution of it.

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Sommario Si considera un sistema L[u]=0 di equazioni alle derivate parziali, quasi lineare (secondo [1]) e di ordine m, il quale sia dotato di qualche bicaratteristica , come accade nel caso iperbolico. Per v=0, , –m(>0) sia u(^v) un'onda di discontinuità di ordine m+v risolvente il detto sistema e avente ipersuperficie di discontinuità contenente Si considerano le relative equazioni di trasporto lungo e si determinano casi interessanti in cui queste equazioni sono mutuamente equivalenti in senso opportuno. Si stabiliscono teoremi di confronto per il trasporto delle discontinuità del tipo suddetto, relative ai sistemi d^hL[u]/dt^h=0 (h=0, , –m) e/o alla linearizazione del sistema L[u]=0 attorno a qualche sua soluzione regolare.

     

A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

A symbolic algorithm is developed for the automatic generation of harmonic balance equations for multitone input for a class of nonlinear differential systems with polynomial nonlinearities. Generalized expressions are derived for the construction of balance equations for a defined multitone signal form. Procedures are described for determining combinations for a given output frequency from the desired set obtained from box truncated spectra and their permutations to automate symbolic algorithm. An application of method is demonstrated using the well-known Duffing–Van der Pol equation. Then the obtained analytical results are compared with numerical simulations to show the accuracy of the approach. The computation times for both the numerical solutions of equations versus the number of frequency components and the symbolic generation of the equations versus the power of nonlinearity are also investigated.     

Stokes＇ first problem for the fourth order fluid in a porous half space

In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy’s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed. The English text was polished by Keren Wang.     

Periodic orbits for the generalized Yang–Mills Hamiltonian system in dimension 6

We apply the averaging theory to study a generalized Yang–Mills Hamiltonian system in dimension $6$ with six parameters. We provide sufficient conditions on the six parameters of the system which guarantee the existence of continuous families of period orbits parameterized by the energy.     

A new method for solving Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system

A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.     

A novel scrape-applied method for the manufacture of the membrane–electrode assembly of the fuel–cell system

This study investigates the transfer of the scrape-applied method from the electrodes of a lithium battery to the membrane-electrode assembly of fuel cells, including Proton Exchange Membrane Fuel Cells and Direct Methanol Fuel Cell. Three methods are commonly used to manufacture lithium battery electrodes： the roller-applied method, the spraying-applied method, and the scrape-applied method. This study develops novel scrape-applied equip- ment for lithium battery electrodes. This method is novel and suitable for producing fuel cell, better than other tradi- tional methods. In this study, the stability of coating process was tested by measuring the weight and thickness of a dry electrode. The stability and reproducibility of electrode fab- rication were examined by systematic data analysis. Finally, the study used a specially designed single cell composed of 16 conductive segments, which are insulated locally. The current passing through each segment was measured using Hall Effect sensors connected to the segment compartments. Based on the measured distribution of the local current in a segmented single cell, the influence of flooding and stoi- chiometry variation of feed gas was discussed in terms of electrochemical reaction rate. The experimental results serve as an important basis for future research in this field, which hold potential benefits to the academia and the industry.     

A new perturbation procedure for limit cycle analysis in three-dimensional nonlinear autonomous dynamical systems

By introducing a new parametric transformation and a suitable nonlinear frequency expansion, the modified Lindstedt–Poincaré method is extended to derive analytical approximations for limit cycles in three-dimensional nonlinear autonomous dynamical systems. By considering two typical examples, it can be seen that the results of the present method are in good agreement with those obtained numerically even if the control parameter is moderately large. Moreover, the present prediction is considerably more accurate than some published results obtained by the multiple time scales method and the normal form method.     

Evidence for re-entrant behavior in laponite–PEO systems

We observe evidence of re-entrant behavior in dispersions of a discotic clay, laponite, with added polymer. Under basic conditions, neat laponite forms a disordered colloidal glass. Rheologically, this phase behaves as a viscoelastic solid, and dynamic light scattering shows evidence of non-ergodic behavior. Addition of low molecular weight poly(ethylene oxide) (PEO) melts the glass, resulting in a low-viscosity liquid with fast dynamics. We believe this is due to a depletion force caused by excess PEO chains in solution. A viscoelastic solid is re-formed with the addition of high molecular weight PEO, which we believe to be caused by polymer chains bridging between laponite particles. The physics in our system is quite different from the hard sphere/nonadsorbing polymer systems for which re-entrant glass transitions have been reported in the literature; however, we believe there may be similarities between these phenomena. To our knowledge, this is the first evidence of a type of re-entrant behavior in anisotropic colloids.     

On the shock–vortex interaction in Schardin's problem

In this study we revisit Schardin's problem by investigating experimentally shock waves diffracting over a finite wedge and interacting with the tip vortices in a complicated manner. Holographic interferometry and shadowgraphy were used in a shock tube for a shock Mach number . Numerical simulations were carried out to obtain complementary flow data. The experimental results show that diverging acoustic waves are generated due to the interaction between shock waves and vortexlets along the slip layer. By means of the computational results obtained for short time intervals, and the corresponding optical images, analysis of the shock-vortex interactions became possible for extended time periods. Received 18 May 1998 / Accepted 4 March 1999     

Soliton solutions for the reduced Maxwell–Bloch system in nonlinear optics via the N-fold Darboux transformation

Under investigation in this paper is the reduced Maxwell?CBloch system, which describes the propagation of the intense ultra-short optical pulses through a two-level dielectric medium. Through symbolic computation, conservation laws are derived and N-fold Darboux transformation (DT) is constructed for that system. By virtue of the DT obtained, multi-soliton solutions are generated. Figures are plotted to reveal the following dynamic features of the solitons: (1) Elastic interactions between two bright one-peak solitons, between two bight two-peak solitons and between two dark two-peak solitons; (2) Parallel propagations between two bright one-peak solitons, between two bright two-peak solitons and between two dark two-peak solitons; (3) Periodic propagations of hump solitons, of a pair of bound hump solitons with the same amplitude and of dark solitons.     

A dynamic Parrondo’s paradox for continuous seasonal systems

Nonlinear Dynamics - We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo’s dynamic paradox, in which the...     

Solve a contact problem by optimization method—to calculate the stresses for the softwheel in a harmonic gear

It is difficult to solve the contact problem by usual finite element program. In this paper, we express the contact problem as an optimization problem. In this form we do not need to know all boundary condition in advance. We only need to know the constraint conditions. This method is especially good for solving contact problem. Using this method, we calculate the stresses of the softwheel in the harmonic gear given by Shanghai Jiaotong University, and the results are in good agreement with the experimental results.