Practical techniques for a three‐dimensional FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundle

Two practical techniques are proposed in this paper to simulate a flow contained in a plenum with a downstream tube bundle under a PC environment. First, a technique to impose slip wall conditions on smooth‐faced planes and sharp edges is proposed to compensate for the mesh coarseness relative to boundary layer thickness. In particular, a new type of Poisson equation is formulated to simultaneously satisfy both such velocity boundary conditions on walls and the incompressibility constraint. Second, a numerical model for a downstream tube bundle is proposed, where hydraulic resistance in a tube is imposed as a traction boundary condition on a fluid surface contacting the tube bundle end. The effectiveness of the techniques is numerically demonstrated in the application to a flow in a condenser water box. Copyright © 2001 John Wiley & Sons, Ltd.     

Ductile–brittle transitions in the fracture of plastically deforming,adhesively bonded structures. Part II: Numerical studies

To enable the effective and reliable use of structural adhesive bonding in automotive applications, the cohesive properties of a joint need to be determined over a wide range of loading rates. In this paper, a strategy for determining these properties has been described and used to analyze a set of experimental results presented in a companion paper. In the particular system studied, a crack growing in a toughened quasi-static mode could make a catastrophic transition to a brittle mode of fracture. The cohesive parameters for both the toughened and brittle modes of crack growth were determined by comparing numerical predictions from cohesive-zone simulations to the results of experimental tests performed using double-cantilever beam specimens and tensile tests. The cohesive parameters were found to be essentially rate-independent for the toughened mode, but the toughness dropped by a factor of four upon a transition to the brittle mode. The results of wedge tests were used as an independent verification of the cohesive parameters, and to verify that the quasi-static properties remained rate-independent to very high crack velocities corresponding to conditions of low-velocity impact. The effects of friction, and the use of the wedge test to determine cohesive parameters, were also explored.     

Construction of the Exact Solution to a Torsion Problem for an Elastic Shaft of Variable Cross Section

The exact solution is constructed to a torsion problem for a circular elastic shaft in a medium referred to a spherical coordinate system. One end of the shaft is rigidly fixed and the other is subjected to either tangential forces or a torque. New integral transforms are obtained to solve the problem.     

A Computational Algorithm for Second-Moment Closure Turbulence Modelling

A computational formulation is proposed for second-moment closure turbulence models, especially suited to models intended to ensure physical realizability. It enables to cast the quite complicated model equations in a compact form. It is specifically applied here to a two-dimensional parabolized flow, though it lends itself to extension to more complex flows. An effective computational algorithm is proposed, based on a staggered grid and a block tridiagonal solver. The algorithm is applied to a turbulent mixing layer, and the comparison between the predictions obtained by standard modelling tools and a realizable second-moment closure clearly points out the superiority of the latter.     

Cone penetration resistance equation as a function of the clay ratio, soil moisture content and specific weight

The cone penetrometer is a simple versatile device which is widely used to monitor the strength of a soil in terms of its resistance to the penetration of a standard cone. The soil penetration resistance is a function of soil moisture content, soil specific weight and soil type. The soil type is characterised by means of a clay ratio which is the ratio of the clay content of the soil to the content of silt and sand.Based on the classical bearing capacity theories for strip foundations, a general cone penetration resistance equation is developed to represent the variability of cohesion and friction angle by means of soil type and moisture content. The empirical relationship is shown to give an accurate prediction of the cone penetration resistance for a wide range of soils from a loamy sand to a heavy clay (clay ratios 0.10–1.60) and over a wide spectrum of soil moisture contents from 10 to 65% w/w.     

Stress-Sensitive Permeability: Application to Fault Integrity During Gas Production

The objective is to propose a simple theoretical approach and the associated numerical algorithm to capture the permeability evolution within a fractured region in response to a stress perturbation. The stress range of interest is typical of a reversible deformation such that the fractures have varying apertures but constant lengths and densities. It is the permeability evolution from a negligible value characteristic of flows on geological times to values more relevant for gas production which is important for the structural integrity of the fractured region. A simple 1D application related to the sealing capacity of a fault bounding a producing gas reservoir is proposed to illustrate the theory. The stress change on the two sides of the faults is obtained with a 2D finite-element simulation based on the theory of poro-elasticity and considering the fault as a material discontinuity. The 1D flow simulation is done in a second step, and the flux is assumed to occur through the fault thickness from the non-depleted (minus side) to the depleted (plus side) regions. It is shown how the depletion results in the fractures opening in the fault damaged zone close to the minus side and the fracture closure next to the plus side. This evolution could be non-monotonic in time because of the development and the thinning of a boundary layer in the fluid pressure at the plus side. The simulations end once a Coulomb criterion is reached, typically at the minus side of the fault. The presence of a low-permeability core in the fault center does not change these conclusions although a positive effective normal stress is detected in the damaged zone on the minus side of the core prior to the Coulomb criterion activation.     

Integral formulation for a circular cylindrical cavity in infinite solid and a finite length coaxial cylindrical crack compressed axially

A method for solving problems of fracture of an infinite solid with a circular cylindrical cavity and a coaxial cylindrical crack near the surface under an uniform axial compression is proposed using a non-classical criterial approach associated with a mechanism of a local stability loss near the defect. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a system of linear algebraic equations with respect to the contraction parameter.     

On a Pseudo-Differential Equation¶for Stokes Waves

It is shown that the existence of a smooth solution to a nonlinear pseudo-differential equation on the unit circle is equivalent to the existence of a globally injective conformal mapping in the complex plane which gives a smooth solution to the nonlinear elliptic free-boundary problem for Stokes waves in hydrodynamics. A dual formulation is used to show that the equation has no non-trivial smooth solutions, stable or otherwise, that would correspond to a Stokes wave with gravity acting in a direction opposite to that which is physically realistic.     

The research on price game model and its complex characteristics of triopoly in different decision-making rule

Based on a detailed analysis of the international market, we establish a decentralized dynamics model to describe the situation that a new oligarch wishes to enter into a market which has been occupied by two oligarchs, so they have different decision rules. Then we establish and analyze the corresponding continuity system, and in detail discuss the Lyapunov exponent of this system, studying the influence of the parameter’s change to the Lyapunov exponent in three situations. Proceeding to the next step, we make the analysis of the complex dynamics behavior, such as Hopf bifurcation, chaos attractor and initial sensibility. We make a numerical simulation under different conditions, and the result shows that the process of game will tend to a Nash equilibrium at a lower price adjustment speed, and with the increase of the value, the system will appear to be unstable and go into a chaos state gradually. However, for the new entrant, the influence of chaos is not huge, and the new entrant can be seen as a stable element in the chaotic market. The research leads to a good guidance to the market with a new entrant to do the best decision-making.     

General Anisotropic Effective Medium Theory for the Effective Permeability of Heterogeneous Reservoirs

One of the techniques to calculate the effective property of a heterogeneous medium is the effective medium theory. The present paper presents a general mathematical formulation for the effective medium approximation using a self-consistent choice of the effective permeability, to apply it to the case of a general anisotropic 2D medium and to the case of a 3D isotropic medium with randomly oriented ellipsoidal inclusions. The 2D results are compared with analytical results and with a homogenization technique with good result. The 3D correlations are used to derive percolation thresholds in two-phase systems with a large permeability contrast, which are compared to numerical results from the literature, also with good results.     

Non-Contact Eddy Current Excitation Method for Vibration Testing

When a conductive material is subjected to a time changing magnetic field, eddy currents are induced in that structure. The eddy currents circulate inside the conductor resulting in a magnetic field that interacts with the applied field. The eddy current field is such that it opposes the change in flux resulting in a force between the source and conductor. The time changing magnetic field necessary to induce an electrometric force in the materials can be generated through a variety of different ways. In the present study, a permanent magnet will be mounted to the tip of an electromagnetic shaker such that the motion of the magnet relative to the structure will cause a time changing field and the formation of eddy currents. The actuator will be demonstrated to be beneficial due to its ability to apply actuation forces without contacting the structure. This study will show that the non-contact nature of the system eliminates mass loading and added stiffness which are downfalls of traditional excitation techniques. Additionally, it will be shown that the use of a non-contact device preserves the mode shapes of the structure, whereas a stinger results in distortions due to the added constraint. Using this concept, a model of the actuation system will be developed, allowing the beams response to be simulated. The actuation system will then be used to excite a cantilever beam to obtain the modal parameters without contacting the structure. The novel non-contact actuation system developed in this paper provides a new method performing vibration testing of on lightweight or flexible structures while preserving their dynamics.     

The Characteristic Response of Hollow Cones

The response of a solid cone to a pure bending moment applied at its tip was found recently in terms of spherical polar coordinates by a using a suitable change of parameter leading to series solutions. By a very simple further parameter change, the additional solutions have been found which are needed to extend the analysis to give the response of a hollow cone to any resultant load applied to its tip. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Nonlinear Temporal Headway Model of Traffic Dynamics

In order to describe the dynamics of a group of road vehicles travelling in a single lane, car-following models attempt to mimic the interactions between individual vehicles where the behaviour of each vehicle is dependent upon the motion of the vehicle immediately ahead. In this paper we investigate a modified car-following model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value. In contrast to our earlier work, a desired time separation between vehicles is used rather than simply being a constant desired distance. In addition, we extend our previous work to include a non-zero driver vehicle reaction time, thus producing a more realistic mathematical model of congested road traffic. Numerical solution of the resulting coupled system of nonlinear delay differential equations is used to analyse the stability of the equilibrium solution to a periodic perturbation. For certain parameter values the post-transient response is a chaotic (non-periodic) oscillations consisting of a broad spectrum of frequency components. Such chaotic motion leads to highly complex dynamical behaviour which is inherently unpredictable. The model is analysed over a range of parameter values and, in each case, the nature of the response is indicated. In the case of a chaotic solution, the degree of chaos is estimated.     

Control of Tollmien�CSchlichting instabilities by finite distributed wall actuation

Tollmien?CSchlichting waves are one of the key mechanisms triggering the laminar-turbulent transition in a flat-plate boundary-layer flow. By damping these waves and thus delaying transition, skin friction drag can be significantly decreased. In this simulation study, a wall segment is actuated according to a control scheme based on a POD-Galerkin model driven extended Kalman filter for state estimation and a model predictive controller to dampen TS waves by negative superposition based on this information. The setup of the simulation is chosen to resemble actuation with a driven compliant wall, such as a membrane actuator. Most importantly, a method is proposed to integrate such a localized wall actuation into a Galerkin model.     

Dynamic shakedown of elastic-plastic solids for a set of alternative loading histories

The paper deals with dynamic shakedown of an elastic-perfectly plastic solid body subjected to a loading history which is unknown but is allowed to belong to a given set of loading histories. In the hypothesis of a piecewise linear convex set, a sufficient shakedown theorem is given and a bounding principle for the plastic work produced is formulated in terms of the dynamic elastic responses to a discrete set of loading histories. The solution of a minimization problem gives the most stringent bound which also proves to possess a local character, i.e., it regards the plastic work density at any point.     

Perturbation analysis of an undulating free surface in a multi-layered structure

This paper presents an analysis of the effect of an undulating free surface on the stress state in a multi-layered structure with an arbitrary number of layers. We present a simple procedure to derive in terms of stress functions the first-order perturbation solution for a multi-layered structure subjected to residual stresses and to external edge loads. The solution is valid for undulation amplitudes that are small compared to undulation wavelength, and it reproduces results reported earlier for homogeneous materials and bi-layers. Using this perturbation solution, the stability of a stressed undulating surface with a given surface energy is evaluated. This analysis leads naturally to the definition of a critical undulation wavelength above which undulations are preferred energetically over a flat surface. The results obtained in the perturbation analysis can be applied to surface diffusion/etching problems in multi-layered structures and to a range of other engineering problems related to undulating surfaces and surface stability.     

Two-Dimensional Mapping of In-plane Residual Stress with Slitting

This paper describes the use of slitting to form a two-dimensional spatial map of one component of residual stress in the plane of a two-dimensional body. Slitting is a residual stress measurement technique that incrementally cuts a thin slit along a plane across a body, while measuring strain at a remote location as a function of slit depth. Data reduction, based on elastic deformation, provides the residual stress component normal to the plane as a function of position along the slit depth. While a single slitting measurement provides residual stress along a single plane, the new work postulates that multiple measurements on adjacent planes can form a two-dimensional spatial map of residual stress. The paper uses numerical simulations to develop knowledge of two fundamental problems regarding two-dimensional mapping with slitting. The first fundamental problem is to estimate the quality of a slitting measurement, relative to the proximity of a given measurement plane to a free surface, whether that surface is the edge of the original part or a free surface created by a prior measurement. The second fundamental problem is to quantify the effects of a prior slitting measurement on a subsequent measurement, which is affected by the physical separation of the measurement planes. The results of the numerical simulations lead to a recommended measurement design for mapping residual stress. Finally, the numerical work and recommended measurement strategy are validated with physical experiments using thin aluminum slices containing residual stress induced by quenching. The physical experiments show that two-dimensional residual stress mapping with slitting, under good experimental conditions (simple sample geometry and low modulus material), has precision on the order of 10 MPa. Additional validation measurements, performed with x-ray diffraction and ESPI hole drilling, are within 10 to 20 MPa of the results from slitting.     

Crack kinking in a piezoelectric solid

The intrinsic coupling between the mechanical and the electric fields assigns a uniquefeature for the fracture in a piezoelectric solid. We model the kink of a crack by continuousdistribution of edge dislocations and electric dipoles. The problem admits an approach based onthe Stroh formalism. A set of coupled singular integral equations are derived for the dislocationand electric dipole density functions associated with a kinked crack. Numerical results indicatethat the crack tends to propagate in a straight line under a tensile stress and a positive electricfield. For a crack subjected to the mixed mode mechanical loading, a superimposed positiveelectric field tends to reduce the kink angle. The influence of the non-singular T-stress-chargeparallel to a crack is also investigated. It is shown that a transverse tensile stress or a positivetransverse electric field will lead to further deviation of the kinked crack from the crackextension line.     

The influence of forward speed on ship motions in abnormal waves: Experimental measurements and numerical predictions

Ship encounters with abnormal waves are increasingly well documented and it is therefore important to be able to model such encounters in order to assess the risks involved and whether there is a requirement for more stringent design rules.This paper presents the results of an experimental investigation into the influence of abnormal waves on a vessel travelling with forward speed in irregular seas. The vessel studied in this case is a naval frigate travelling at a range of speeds. To put the motions measured in abnormal waves into context comparisons are made to those in random seas with a variety of significant wave heights, both non-severe and severe. A further objective is to compare experimental measurements with motion predictions from both a two-dimensional linear strip theory and a three-dimensional partly nonlinear seakeeping model.Results demonstrate that abnormal waves may not necessarily be the worst conditions that a ship can encounter. However, accelerations derived from the rigid body motions appear to be in excess of rules values. This has implications for design due to the unexpected nature of abnormal wave occurrence and the consequent likelihood of encountering such a wave at a higher speed (hence in a more severe operating condition) than a random sea of an equivalent height.The three-dimensional partly nonlinear model demonstrates improved agreement with experimental measurements of rigid body motions, compared to the two-dimensional strip theory. It is therefore considered to have greater potential as a design tool for abnormal wave encounters. Further validation with a wide range of sea states and vessel types is required.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.