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The paper aims to present an experimental and numerical investigation of the load–settlement behavior of soil reinforced by stone column, as well as to evaluate the plane strain unit cell model for the analysis of stone columns.

The numerical analysis was done using both axisymmetric and plane strain models. The elastic perfectly plastic behavior of Mohr–Coulomb was adopted for both soil and column material. The numerical results of this study were validated by the comparison with the in-situ measurements of a full-scale loading test on a stone column. This study also evaluated the effect of different parameters involved in the design of a stone column, including Young’s modulus of the column material, column diameter, spacing between the stone columns and Poisson’s ratio of the column material.

After the numerical simulation, the results from both axisymmetric and plane strain models are quite comparable. In addition, the numerical results revealed that the stone column with low spacing, a large diameter and a high Young’s modulus indicated better behavior against the settlement.

The axisymmetric unit cell model was used in many numerical studies on the behavior of stone columns. In the present work, a field load test on stone column was simulated using a plane strain unit cell model. This research adds that the plane strain unit cell model can be used to predict the settlement of reinforced soil with stone columns.

In the finite element method two options are currently available for dealing with problems involving an axisymmetric geometry but in which loads, displacements or other boundary conditions do not have rotational symmetry. The first involves a full three‐dimensional solution whereas the second is to use a two‐dimensional (2D) axisymmetric formulation and to express the non‐symmetric loads/displacements as Fourier series in the circumferential direction. There are some cases, however, that, in spite of not being truly axisymmetric, it can be shown that the non‐zero components of the full strain tensor number four or less. In this paper it is shown that such problems may be solved using simple 2D finite element formulations and two alternative solution methods are presented. One of these involves a modification to the matrix relating strains to displacements and the second employs conventional 2D formulations with tied degrees of freedom. The solution procedures are applied to three examples which have some geotechnical interest, namely the behaviour of a long rigid pile under either torsional or vertical loading and the behaviour of a hollow cylinder sample subjected to torsion. In all three cases the soil is modelled by means of an elastoplastic constitutive law of the Cam‐clay type.

The purpose of this paper is to present the results of an analysis performed to study unsteady mixed convection at the stagnation point flow over a plate moving along the direction of flow impingement. The similarity transformations are used to transform the governing nonlinear partial differential equation to a system of an ordinary differential equation.

The transformed equations are then solved numerically by a shooting technique together with bvp4c function.

The numerical results are compared with the corresponding results from previous researchers. The effects of the unsteadiness Parameter A, Prandtl number Pr, mixed convection parameter λ for plane (m = 0) and axisymmetric (m = 1) flow on the shear stress or the skin friction and heat transfer coefficients, as well as the velocity and temperature profiles, are presented and discussed.

Dual solutions for the opposing flow and multiple solutions for the assisting flow are found.

This paper aims to examine how using lattice Boltzmann method (LBM) aids the study of the isothermal‐gas flow with slight rarefaction in long microtubes.

A revised axisymmetric lattice Boltzmann model is proposed to simulate the flow in microtubes. The wall boundary condition combining the bounce‐back and specular‐reflection schemes is used to capture the slip velocity on the wall. Appropriate relation between the Knudsen number and relax‐time constant is defined.

The computed‐slip velocity, average velocity and non‐linear pressure distribution along the microtube are in excellent agreement with analytical solution of the weakly compressible Navier‐Stokes equations. The calculated‐friction factors are also consistent with available experimental data. For simulations of slip flow in microtube, LBM is more accurate and efficient than DSMC method.

The laminar flow in circular microtube is assumed to be axisymmetric. The present LBM is only applied to the simulation of slip flows (0.01 < Kn₀<0.1) in microtube.

Lattice‐BGK method is a very useful tool to investigate the micro slip flows.

A revised axisymmetric D2Q9 lattice Boltzmann model is proposed to simulate the slip flow in axisymmetric microtubes.

This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF laboratory. FORGE3 is a three‐dimensional finite element computer program that can simulate hot forging of industrial parts. The flow problem is solved using a thermomechanical analysis. The mechanical resolution and the thermal one are coupled by the way of the consistency K which is thermodependent, the plastic deformation in the volume of the material and the friction heat flux on the surface. The material behaviour is assumed to be incompressible and viscoplastic (Norton—Hoff law) with the associated friction law. The thermal resolution includes the case of non‐linear physical properties and boundary conditions. An explicit Euler scheme is used for the mechanical resolution and two‐step schemes for the thermal one. For the computation of other parameters, it is necessary to have a good approximation for the strain rate tensor. The Orkisz method has been used to determine the deviatoric stress tensor and p is calculated by an original smoothing method. The results show that it is possible to get good information on the flow and on the physical properties during forging of automotive parts. Comparisons have been made with experimental measurements with a reasonably good agreement.

A new numerical method is presented for the simulation of flows of incompressible fluids in plane or axisymmetric flows. Under certain assumptions, the physical domain can be transformed into a rectangular domain. This method can involve free surface flow problems. In Newtonian and non‐Newtonian cases, the relevant equations are non‐linear and the solution is carried out in the transformed domain where the stream lines are parallel straight lines.

A finite element procedure is presented for refined transient analysis of two‐dimensional (plane or axisymmetric) non‐linear structures involving arbitrarily large displacements, rotations and strains. The finite element model is based on the biquadratic nine‐node element of the Lagrange family. The relevant points pertaining to the equations of motion and their integration and to the spatial description, including geometrical and material non‐linearities, are considered. In particular, stress and strain rates are discussed. Finally, significant numerical applications show the effectiveness of the proposed method.

A radial offset jet has the flow characteristics of a radial jet and an offset jet, which are encountered in many engineering applications. The purpose of this paper is to study the dynamics and mass transfer characteristics of the radial offset jet with an offset ratio 6, 8 and 12.

Three turbulence models, namely the SST k-? model, detached eddy simulation model, and improved delayed detached eddy simulation (IDDES), were applied to the radial offset jet with an offset ratio eight and their results were compared with experimental results. The contrasting results, such as the distributions of mean and turbulent velocity and pressure, show that the IDDES model was the best model in simulating the radial offset jet. The results of the IDDES were analyzed, including the Reynolds stress, turbulent kinetic energy, triple-velocity correlations, vertical structure and the tracer concentration distribution.

In the axisymmetric plane, Reynolds stresses increase to reach a maximum at the location where the jet central line starts to be bent rapidly, and then decrease with increasing distance in the radial direction. The shear layer vortices, which arise from the Kelvin-Helmholtz instability near the jet exit, become larger scale results in the entrainment and vortex pairing, and breakdown when the jet approaches the wall. Near the wall, the vortex swirling direction is different at both front and back of attachment point. In the wall-jet region, the concentration distributions present self-similarity while it keeps constant below the jet in the recirculation region.

The radial offset jet with other offset ratio and exit angle is not considered in this paper and should be investigated.

The results obtained in this paper will provide guidance for studying similar flow and a better understanding of the radial offset jet.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to provide an axisymmetric model of tube hydroforming using a Fourier Series based finite element method.

Fourier series interpolation function, which considerably reduces the size of the global stiffness matrix and the number of variables, is employed to approximate displacements. The material of the tube is assumed to be elastic‐plastic and to satisfy the plasticity model that takes into account the rate independent work hardening and normal anisotropy. Numerical solution obtained from an updated Lagrangian formulation of the general shell theory is employed. The axial displacement stroke (a.k.a. axial feed) during tube hydroforming is incorporated using Lagrange multipliers. Contact constraints and boundary friction condition are introduced into the formulation based on the penalty function, which imposes the constraints directly into the tangent stiffness matrix. A forming limit curve based on shear instability and experimental measurements are used as fracture criteria.

The results obtained from this new formulation are compared against the nonlinear finite element code ABAQUS and experimental measurements for isotropic and transversely anisotropic tube materials. The hoop and axial strains predicted with AXHD code compared excellently with those from ABAQUS FEM code using plane stress axisymmetric (SAX1) and four‐node shell (S4R) elements. However, in the case of aluminum, the numerically predicted maximum hoop strain underestimated the actual hoop strain measured from the tube bulging experiment.

The axisymmetric hydroforming program (AXHD) developed in this work is very efficient in simulating the free‐forming stage of the tube hydroforming process under simultaneous action of internal pressurization and displacement stroke.

Although Fourier Series based finite element method has been used in metal forming, the extended application presented in this paper is novel in the finite element analysis of tube hydroforming.