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Numerical simulation of a fluid flow involves the specification of boundary conditions along all or part of the boundary. Designs a means of handling outflow boundary conditions for the incompressible Navier‐Stokes equations. Addresses through‐flow problems involving the specification of outflow conditions at the synthetic boundary. This outflow boundary condition is applicable to a developing flow problem. The underlying objectives behind designing the boundary condition at the truncated boundary are three‐fold, namely: matching with Navier‐Stokes equations inside the domain; taking both non‐linear and diffusive contributions into account; and ensuring the discrete divergence‐free condition. In order to meet these requirements, follows the concept of a free boundary condition by taking the outflow nodal values of u, v and p as unknowns, which are coupled with the interior unknowns through the surface integrals in the momentum equations. The computed solutions can be legitimately regarded as solutions to conservation equations under consideration when both components of the surface traction vector approach zero. With the convergent property accommodated in the present mixed finite element analysis, the task remains to simply improve the accuracy. Demonstrates the capability of the proposed non‐linear outflow boundary conditions through several benchmark tests.

A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are reviewed, classified broadly into two groups, as domain integrals and virtual crack extension techniques. In addition to considerations of how such quantities may be calculated by finite elements, assessment methods of conducting the actual incremental analyses are described.

The purpose of this paper is to numerically study blood flow through a subject‐specific carotid artery with a moderately severe stenosis, also to thoroughly analyse the wall shear stress (WSS), oscillatory shear index (OSI) and WSS angular deviation (WSSAD). One of the important aspects of this study is the investigation on the influence of the extensions attached to the domain outlets.

The segmentation of the carotid artery is carried out using a deformable model based on a level set method. A geometric potential force (GPF) is employed to deform the level set to obtain the carotid artery geometry. The initial surface meshing is generated using an advanced marching cubes (MC) method, before improving the quality of the surface mesh via a number of mesh cosmetic steps. The volume mesh generation has two parts. In the first part, a quasi‐structured, boundary layer mesh is generated in the vicinity of the geometry walls. The second part of the meshing involves unstructured tetrahedral meshing of the inner part of the geometry. After the meshing stage, the flow boundary conditions are generated by numerically solving the Helmholtz equation in both space and time. Finally, the explicit characteristic‐based split (CBS) method is employed in a parallel environment to produce a detailed analysis of wall quantities.

In general, WSS is very high in the vicinity of the carotid artery apex and in the proximity of the stenosis. From the results obtained, it is clear that the influence of outlet domain extension is marginal. While the peak instantaneous WSS differs by a maximum of 5.7 per cent, the time‐averaged WSS difference due to extended domain is only 1.3 per cent. Two other derived parameters are also examined in the paper, the oscillating shear index and the WSSAD. Both these quantities also display minor or negligible differences due to domain extension.

It has been perceived that domain extension is essential to avoid wrong application of boundary conditions. The results obtained, however, conclusively show that the outlet domain extension has only a moderate influence on WSS. Thus, outlet extension to the domains may not be essential for arterial blood flows. It is also observed that the dramatic values of peak WSS obtained near the stenosis is the result of high resolution mesh along with boundary layers used in this study. Both the outcomes represent the originality of this paper.

In metal forming, there are problems with recurrent geometric characteristics and without explicitly prescribed boundary conditions. In such problems, so‐called recurrent boundary conditions must be introduced. The present study deals with non‐steady‐state three‐dimensional finite element analysis for helical extrusion of twisted clover and trocoidal gear sections through a curved die. A boundary‐directed remeshing scheme based on the modular remeshing technique has been proposed to reduce the errors arising in mapping of variables between old and new mesh systems. The computed extrusion pressures in reaching the near steady‐state loading stage are compared with the results of the experiments as well as the steady‐state analysis. The three‐dimensional deformed pattern involving warping at the extruded end due to torsional deformation mode is demonstrated. For twisted clover and trocoidal gear sections, the twisted angle of an extruded product is smaller than that of the die, and the simpler the shape of the sections, the larger the amount of the deviation.

Describes a set of numerical techniques which implement the rate‐dependent multi‐mechanism deformation (M‐D) constitutive model for rock salt in a finite element code for use in three‐dimensional, finite strain simulations of creep closure in deeply buried salt excavations. Presents essential details of the numerical implementation. The constitutive model is exercised in a three‐dimensional closure simulation of a large underground field experiment. Compares results from the simulation against actual closure measurements taken from the experiment.

An optimisation method for design of intermediate die shapes needed in some forging operations is presented. The basic problem consists of finding an optimal two‐step forging sequence by automatically designing the shape of the preforming tools. The optimisation problem is defined based on an inverse formulation. The objective function of the optimisation problem is a function describing the quality of the obtained part by measuring the die underfill. The finite element method is used to simulate the forging problem. The optimisation method is based on a modified sequential unconstrained minimisation technique and a gradient method. The sensitivity‐dependent algorithm requires computing the derivatives of the objective function with respect to the design variables defining the preform shapes. A direct differentiation method has been developed for this purpose. The optimisation scheme is demonstrated with two axisymmetric forging examples in which optimal preform dies are obtained.

This study aims to develop a new analysis approach devised by incorporating a gradient-enhanced microplane damage model (GeMpDM) into isogeometric analysis (IGA), which shows computational stability and capability in accurately predicting crack propagations in structures with complex geometries.

For the non-local microplane damage modeling, the maximum modified von-Mises equivalent strain among all microplanes is regularized as a representative quantity. This characterization implies that only one additional governing equation is considered, which improves computational efficiency dramatically. By combined use of GeMpDM and IGA, quasi-static and dynamic numerical analyses are conducted to demonstrate the capability in predicting crack paths of complex geometries in comparison to FEM and experimental results.

The implicit scheme with the adopted damage model shows favorable numerical stability and the numerical results exhibit appropriate convergence characteristics concerning the mesh size. The damage evolution is successfully controlled by a tension-compression damage factor. Thanks to the advanced geometric design capability of IGA, the details of crack patterns can be predicted reliably, which are somewhat difficult to be acquired by FEM. Additionally, the damage distribution obtained in the dynamic analysis is in close agreement with experimental results.

The paper originally incorporates GeMpDM into IGA. Especially, only one non-local variable is considered besides the displacement field, which improves the computational efficiency and favorable convergence characteristics within the IGA framework. Also, enjoying the geometric design ability of IGA, the proposed analysis method is capable of accurately predicting crack paths reflecting the complex geometries of target structures.

Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM.

The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour.

The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable.

The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

Describes simulations of impact forging processes. Uses the explicit time integration finite element method, which is based on direct time integration of equation of motion, to compute the deformation of the workpiece and the dies. Uses the program developed to simulate the copper blow test performed on a 350,000J counter‐blow hammer. The calculated result reveals a good agreement in the final deformed configurations between the experiment and the explicit simulation. In order to compare this with the explicit method, the implicit time integration rigid‐plastic finite element program considering the inertia effect is also applied to the copper blow test simulation. As a result of the copper blow test simulation using the explicit program and the implicit program, finds that the calculated results have good agreements in available plastic deformation energy, forging load and equivalent plastic strain distribution. Finally, applies the developed program to simulations of multi‐blow forging processes. Presents three major findings from the multi‐blow forging simulations: (1) the continuous analysis technique used for the multi‐blow forging simulations works well; (2) the blow efficiency and the forging load generated by blow operations can be analysed efficiently and simulated results coincide with previous experimental and analytical ones; (3) the geometrical configuration of the workpiece is closely related to blow efficiency.

In this paper, a new density‐stiffness interpolation scheme for topology optimization of continuum structures is proposed. Based on this new scheme, not only the so‐called checkerboard pattern can be eliminated from the final optimal topology, but also the boundary‐smooth effect associated with the traditional sensitivity averaging approach can also be overcome. A proof of the existence of the solution of the optimization problem is also given, therefore mesh independent optimization results can be obtained. Numerical examples illustrate the effectiveness and the advantage of the proposed interpolation scheme.