Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.     

Analysis of the wave solution of the elastokinetic equations of a Cosserat continuum for the case of bulk plane waves

A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 196–203, March–April, 2008.     

Series solution for large deflections of a cantilever beam with variable flexural rigidity

In this paper large deflection and rotation of a nonlinear Bernoulli-Euler beam with variable flexural rigidity and subjected to a static co-planar follower loading is studied. It is assumed that the angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation. The governing equation of this problem is solved analytically for the first time using a new kind of analytical technique for nonlinear problems, namely the Homotopy Analysis Method (HAM). The present solution can be used for the analysis of a wide range of loads, material/cross section properties and lengths for beams undergoing large deformations. The results obtained from HAM are compared with results reported in previous works. Finally, the load–displacement characteristics of a uniform cantilever beam with different material properties under a follower force applied normal to the deformed beam axis are presented.     

Dynamic deformation of a thermoviscoelastic rod of triangular cross section in a coupled formulation

For the coupled model of a thermoviscoelastic rod of equilateral triangular cross section, two exact solutions are obtained for the cases where a normal displacement and a shear stress or a tangential displacement and a normal stress are specified on the lateral surface of the rod. A dimensionless parameter R₀ is introduced to judge the appropriateness of taking into account the coupling in the formulation of the problem. Formulas are given for the velocities and lengths of the temperature, shear, and longitudinal waves, which can be used in experiments to determine the physical properties of thermoviscoelastic materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 128–143, July–August, 2007.     

Wave processes in solids with defects

The propagation of plane harmonic waves in viscoelastic and elastoviscoplastic materials are studied using the equations of the field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. Wave propagation velocities and refraction and absorption coefficients are determined. The structure of the waves and the correlation between the displacement waves and the defect-field waves determining plastic deformation are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 190–197, November–December, 2008.     

Analytical solutions of tsunamis generated by underwater earthquakes

Tsunamis induced by underwater earthquakes are theoretically analyzed by applying the linear potential theory. Special attention is placed on the initial state of tsunami. For instantaneous seabed deformations, analytical wave solutions induced by three fundamental seabed deformations at initial stage are derived rather than integral expressions in past studies. These analytical solutions constitute a fundamental base for analyzing waves generated by arbitrary seabed displacement with the help of Fourier analysis. Tsunamis induced by non-instantaneous seabed deformation are analyzed as well. For the sake of examining the contributions of all wave components involved in the tsunami waveform, the amplitude density is proposed to examine the effects of deformation width, water depth, harmonic mode and rising time on waveforms. Results show that a larger ratio of water depth to deformation width results in a greater difference between initial waveform and seabed deformation, and the effect of the rising time is significant in deeper-water configuration. For cosine and sine seabed liftings, the effects of higher harmonic modes might be ignored.     

A C<Superscript>0</Superscript>-type zig–zag theory and finite element for laminated composite and sandwich plates with general configurations

In order to conveniently develop C⁰ continuous element for the accurate analysis of laminated composite and sandwich plates with general configurations, this paper develops a C⁰-type zig–zag theory in which the interlaminar continuity of transverse shear stresses is a priori satisfied and the number of unknowns is independent of the number of layers. The present theory is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. On the premise of retaining the merit of previous zig–zag theories, the derivatives of transverse displacement have been taken out from the displacement fields. Therefore, based on the proposed zig–zag theory, it is very easy to construct the C⁰ continuous element. To assess the performance of the proposed model, the classical quadratic six-node triangular element with seven degrees of freedom at each node is presented for the static analysis of laminated composite and sandwich plates. The typical examples are taken into account to assess the performance of finite element based on the proposed zig–zag theory by comparing the present results with the three-dimensional elasticity solutions. Numerical results show that the present model can produce the more accurate deformations and stresses compared with the previous zig–zag theories.     

Solution of strongly nonlinear problems in the mechanics of a solid deformable body

A new algorithm for constructing a Lagrangian formulation of the incremental theory on the basis of finite-element digitization of the equilibrium equations of strongly nonlinear mechanical systems subject to static loads is proposed. Example solutions of problems of nonlinear deformation of a solid that confirm the validity of the applied relations between increments in stresses and increments in deformations is presented. Technical University of Construction and Architecture, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 22–26, March, 1999.     

Accounting for the elastic properties of a non-Newtonian material under its viscosimetric flow

This paper considers the deformation and viscoplastic flow of a non-Newtonian material enclosed between coaxial rigid cylindrical surfaces, each of which performs a rotation followed by a stop and a rotation in the opposite direction. The problem is solved using the model of large elastoviscoplastic deformations, in contrast to the classical solutions obtained using the model of a rigid viscoplastic body. The parameters of the viscosimetric process are calculated in both the region of viscoplastic flow developed and the region of elastic deformation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 143–151, March–April, 2008.     

An Internal Damping Model for the Absolute Nodal Coordinate Formulation

Introducing internal damping in multibody system simulations is important as real-life systems usually exhibit this type of energy dissipation mechanism. When using an inertial coordinate method such as the absolute nodal coordinate formulation, damping forces must be carefully formulated in order not to damp rigid body motion, as both this and deformation are described by the same set of absolute nodal coordinates. This paper presents an internal damping model based on linear viscoelasticity for the absolute nodal coordinate formulation. A practical procedure for estimating the parameters that govern the dissipation of energy is proposed. The absence of energy dissipation under rigid body motion is demonstrated both analytically and numerically. Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green–Lagrange strain–displacement relationship. In addition, the resulting damping forces are functions of some constant matrices that can be calculated in advance, thereby avoiding the integration over the element volume each time the damping force vector is evaluated.     

Existence theorems for a class of Chandrasekhar H-equation with perturbation in transpory theory

In this paper, the existence and approximation theorems of positive solutions in space C[0,1] for a class of Chandrasekhar H-equations with perturbation in transport theory are proved. The results presented in this paper improve and extend some recent results in [1–9]. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Stabilization of solutions of the nonlinear equation of filtration of a two-phase liquid

The asymptotic behavior (with unlimited increase in time) of solutions of boundary-value problems for the filtration equation for a two-phase liquid that describe the displacement of immiscible incompressible liquids from a bed is studied. Convergence of these solutions to the unique solution of the steady problem (stabilization) is established, and, under additional assumptions, the rate of convergence is evaluated. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 30–36, May–JJune, 1999.     

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more-sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.      

Existence of Traveling Waves of Invasion for Ginzburg–Landau-type Problems in Infinite Cylinders

We study a class of systems of reaction–diffusion equations in infinite cylinders which arise within the context of Ginzburg–Landau theories and describe the kinetics of phase transformation in second-order or weakly first-order phase transitions with non-conserved order parameters. We use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation. Our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non-linearities. We also prove boundedness, regularity, and some other properties of the obtained solutions, as well as several sufficient conditions for existence or non-existence of such traveling waves, and give rigorous upper and lower bounds for their speed. In addition, we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized. We give a sample application of our results using a computer-assisted approach.     

On the General Structure of Small on Large Problems for Elastic Deformations of Varga Materials I: Plane Strain Deformations

In three recent papers [6–8], the present authors show that both plane strain and axially symmetric deformations of perfectly elastic incompressible Varga materials admit certain first integrals, which means that solutions for finite elastic deformations can be determined from a second order partial differential equation, rather than a fourth order one. For plane strain deformations there are three such integrals, while for axially symmetric deformations there are two. The purpose of the present papers is to present the general equations for small deformations which are superimposed upon a large deformation, which is assumed to satisfy one of the previously obtained first integrals. The governing partial differential equations for the small superimposed deformations are linear but highly nonhomogeneous, and we present here the precise structure of these equations in terms of a second-order linear differential operator D², which is first defined by examining solutions of the known integrals. The results obtained are illustrated with reference to a number of specific large deformations which are known solutions of the first integrals. For deformations of limited magnitude, the Varga strain-energy function has been established as a reasonable prototype for both natural rubber vulcanizates and styrene-butadiene vulcanizates. Plane strain deformations are examined in this present part while axially symmetric deformations are considered in Part II [16]. This revised version was published online in August 2006 with corrections to the Cover Date.     

Curve cracks lying along a parabolic curve in anisotropic body

ＣＵＲＶＥＣＲＡＣＫＳＬＹＩＮＧＡＬＯＮＧＡＰＡＲＡＢＯＬＩＣＣＵＲＶＥＩＮＡＮＩＳＯＴＲＯＰＩＣＢＯＤＹＨｕＹｕａｎ－ｔａｉ（胡元太）ＺｈａｏＸｉｎｇ－ｈｕａ（赵兴华）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ;ＳｈａｎｇｈａｉＩｎｓｔｉｔｕｔｅｏｆＡ...     

High-speed fiber spinning process with spinline flow-induced crystallization and neck-like deformation

The dynamics and stability of the high-speed fiber spinning process with spinline flow-induced crystallization and neck-like deformation have been studied using a simulation model equipped with governing equations of continuity, motion, energy, and crystallinity, along with the Phan-Thien–Tanner constitutive equation. Despite the fact that a simple one-phase model was incorporated into the governing equations to describe the spinline crystallinity, as opposed to the best-known two-phase model [Doufas et al. J Non-Newton Fluid Mech, 92:27–66, 2000a]; [Kohler et al. J Macromol Sci Phys, 44:185–202, 2005] that treats amorphous and crystalline phases separately in computing the spinline stress, the simulation has successfully portrayed the typical nonlinear characteristic of the high-speed spinning process called neck-like spinline deformation. It has been found that the criterion for the neck-like deformation to occur on the spinline is for the extensional viscosity to decrease on the spinline, so that the spinning is stabilized by the formation of the spinline neck-like deformation. The accompanying linear stability analysis explains this stabilizing effect of the spinline neck-like deformation, corroborating a recent experimental finding [Takarada et al. Int Polym Process, 19:380–387, 2004].This paper was presented at the 2nd Annual European Rheology Conference 2005 on April 21–23, 2005, in Grenoble, France.     

Exact Results for the Homogenization of Elastic Fiber-Reinforced Solids at Finite Strain

This work is concerned with the homogenization of solids reinforced by aligned parallel continuous fibers or weakened by aligned parallel cylindrical pores and undergoing large deformations. By alternatively exploiting the nominal and material formulations of the corresponding homogenization problem and by applying the implicit function theorem, it is shown that locally homogeneous deformations can be produced in such inhomogeneous materials and form a differentiable manifold. For every macroscopic strain associated to a locally homogeneous deformation field, the effective nominal or material stress–strain relation is exactly determined and connections are also exactly established between the effective nominal and material elastic tangent moduli. These results are microstructure-independent in the sense that they hold irrespectively of the transverse geometry and distribution of the fibers or pores. A porous medium consisting of a compressible Mooney–Rivlin material with cylindrical pores is studied in detail to illustrate the general results. This work was the first time presented at the Euromech Colloqium 464 on “Fiber-reinforced Solids: Constitutive Laws and Instabilities”, September 28–October 1, 2004, Cantabria, Spain.     

Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations

This investigation is concerned with the use of an implicit integration method with adjustable numerical damping properties in the simulation of flexible multibody systems. The flexible bodies in the system are modeled using the finite element absolute nodal coordinate formulation (ANCF), which can be used in the simulation of large deformations and rotations of flexible bodies. This formulation, when used with the general continuum mechanics theory, leads to displacement modes, such as Poisson modes, that couple the cross section deformations, and bending and extension of structural elements such as beams. While these modes can be significant in the case of large deformations, and they have no significant effect on the CPU time for very flexible bodies; in the case of thin and stiff structures, the ANCF coupled deformation modes can be associated with very high frequencies that can be a source of numerical problems when explicit integration methods are used. The implicit integration method used in this investigation is the Hilber–Hughes–Taylor method applied in the context of Index 3 differential-algebraic equations (HHT-I3). The results obtained using this integration method are compared with the results obtained using an explicit Adams-predictor-corrector method, which has no adjustable numerical damping. Numerical examples that include bodies with different degrees of flexibility are solved in order to examine the performance of the HHT-I3 implicit integration method when the finite element absolute nodal coordinate formulation is used. The results obtained in this study show that for very flexible structures there is no significant difference in accuracy and CPU time between the solutions obtained using the implicit and explicit integrators. As the stiffness increases, the effect of some ANCF coupled deformation modes becomes more significant, leading to a stiff system of equations. The resulting high frequencies are filtered out when the HHT-I3 integrator is used due to its numerical damping properties. The results of this study also show that the CPU time associated with the HHT-I3 integrator does not change significantly when the stiffness of the bodies increases, while in the case of the explicit Adams method the CPU time increases exponentially. The fundamental differences between the solution procedures used with the implicit and explicit integrations are also discussed in this paper.     

Centrifugal experimental study of suction bucket foundations under dynamic loading

Centrifugal experiments were carried out to investigate the responses of suction bucket foundations under horizontal and vertical dynamic loading. It is shown that when the loading amplitude is over a critical value, the sand at the upper part around the bucket is softened or even liquefied. The excess pore pressure decreases from the upper part to the lower part of the sand layer in the vertical direction and decreases radially from the bucket’s side wall in the horizontal direction. Large settlements of the bucket and the sand layer around the bucket are induced by dynamic loading. The dynamic responses of the bucket with smaller height (the same diameter) are heavier. The project supported by the fund of Chinese Ocean Oil Co. and Chinese Academy of Sciences(KZCX2-YW-302-02).