A finite element/nodal volume technique for flow simulation of injection pultrusion

In this paper, a finite element/nodal volume technique is developed to simulate the resin flow through the reinforcement during injection pultrusion processes. The governing equations for the pressure distribution and the conservation of resin mass during injection pultrusion are first derived. The solution algorithm and its numerical implementation are described. In particular, an algorithm is developed to advance the flow front by taking into account both the resin flow relative to the reinforcement and the movement of the pultruded part as a whole. The numerical technique developed is validated against a one-dimensional analytical solution derived. A number of numerical tests are then conducted to investigate the numerical performance and capability of the technique.     

Deep rolling of fine blanking punch edges

Fine blanking is an economical process to manufacture components with a high sheared edge quality. Fine blanking of high-strength steels leads to an increase of the wear of fine blanking punches and deteriorates the economical efficiency of this process. In preliminary work lateral surfaces of cylindrical punches made of different hardened steels industrially used for tool manufacturing were deep rolled. Under proper process parameters a reduction of surface roughness, a hardness increase as well as an induction of compressive residual stresses in the surface layer were achieved. Therefore, deep rolling has a potential to improve the wear resistance of fine blanking punches. In order to improve the quality of the sheared edge of a workpiece, fine blanking punches must have a round fillet on the cutting edge. Filleting through plastic deformation can improve the wear resistance of this most loaded region of the fine blanking punch. In order to perform the filleting of the cutting edge through plastic deformation and to induce strain hardening and compressive residual stresses into the edge region a novel profiled deep rolling tool is developed in this work. Furthermore, the technical feasibility of the edge deep rolling with regard to the processing of fine blanking punches is assessed for the first time. The approach is based on a numerical modeling and experimental investigation of edge deep rolling.     

A control volume finite element method for adaptive mesh simulation of flow in heap leaching

We construct a mathematical model for the time-dependent flow of a simple liquid through a conical porous filter, driven solely by hydrostatic pressure. The model is relevant to the conical paper filter used in chemistry laboratories as a separation device and also to the common drip coffee maker. Employing a variety of simplifying assumptions, we find closed form, albeit approximate, expressions for the time-varying liquid level in the cone, the final positional distribution of solute, such as the coffee grounds, on the filter, and the average residence time of the liquid in the cone. This last quantity could be associated with the strength of the coffee brew. Perhaps surprisingly, we find that the residence time is independent of both the volume of liquid used and also the rate of pouring, provided the latter is sufficiently slow.     

The finite element method for laminar flow with chemical reaction

A finite element formulation of laminar flow with finite rate chemical reaction and heat release is made. Results are presented for steady flow in a channel, a special case of which is solved analytically, and for transverse flow around a cylinder. These illustrate the power of the finite element method for the calculation of reacting flows in complex geometries.     

Implicit solid,flow and flow–solid finite element approaches in blade forging simulation

A comparative theoretical and numerical study of the flow (rigid‐plastic) and solid (elasto‐plastic, in rate form) simulation approaches applied to the isothermal blade forging process for closing and opening of the dies is presented. In the rigid‐plastic approach the solution is followed by an elasto‐plastic solution in unloading (opening of the dies). The deformation of the billet, effective plastic strains and stresses were compared between the two solutions in the closing of the dies and when the dies were opened. Furthermore, the flow–solid approach was used in simulating the process and then the results, including the time–load and time–volume curves, were compared with previous results. The cost was lower and the efficiency was superior in the suggested flow–solid approach. Copyright © 2003 John Wiley & Sons, Ltd.     

A stable finite element simulation of convective transport

A finite element simulation of the equations of momentum and energy transport in fluids has been implemented with triangular elements. An attempt is made to single out the reasons for numerical instabilities reported by other investigators for convection–diffusion transport operations in fluid mechanics when the ratio of the convective to the diffusive terms, measured by the Reynolds and Peclét numbers, is of the order of a hundred. To this end, the equations are solved for several problems to permit a direct comparison with results of other formulations. It is shown that the appearance of instability can be delayed by a proper choice of boundary conditions, and its intensity can be reduced through the use of triangular finite elements. Results agree very well with theoretical solutions for particular test problems including flows with large convection effects, large dissipation effects and fluids with temperature dependent properties.     

热冲盂成形过程的刚粘塑性有限元模拟

采用刚粘塑性有限元法对热冲盂成形过程进行了数值模拟.讨论了刚粘塑性有限元法,并分析了热冲盂成形工艺的模拟结果.     

Numerical simulation of elastic plastic fatigue crack growth in functionally graded material using the extended finite element method

In the present work, the extended finite element method has been used to simulate the fatigue crack growth problems in functionally graded material in the presence of holes, inclusions, and minor cracks under plastic and plane stress conditions for both edge and center cracks. Both soft and hard inclusions have been implemented in the problems. The validity of linear elastic fracture mechanics theory is limited to the brittle materials. Therefore, the elastic plastic fracture mechanics theory needs to be utilized to characterize the plastic behavior of the material. A generalized Ramberg-Osgood material model has been used for modeling purposes.     

Fragmentation algorithm for finite element failure simulation and analysis

An algorithm which combines the techniques of numerical analysis and numerical simulation in the study of transient dynamic structural response is proposed. This is achieved by incorporating the ability to create new surfaces and separate fragments according to a defined failure criterion into a finite element procedure which uses explicit time integration. Thus, the algorithm not only provides accurate prediction of the structural failure and fragmentation pattern, but also evaluates accurate stress, velocity, acceleration and displacement values of each fragmented component. To develop a viable fragmental algorithm, other than the expected modification in storage and node bookkeeping, we found it necessary to introduce an efficient algorithm to handle extremely large displacements resulting from the fracture. In that regard, an updated corotational approach is introduced.     

A 3D finite element approach for the coupled numerical simulation of electrochemical systems and fluid flow

A comprehensive finite element method for three‐dimensional simulations of stationary and transient electrochemical systems including all multi‐ion transport mechanisms (convection, diffusion and migration) is presented. In addition, non‐linear phenomenological electrode kinetics boundary conditions are accounted for. The governing equations form a set of coupled non‐linear partial differential equations subject to an algebraic constraint due to the electroneutrality condition. The advantage of a convective formulation of the ion‐transport equations with respect to a natural application of homogeneous flux boundary conditions is emphasized. For one of the numerical examples, an analytical solution for the coupled problem is provided, and it is demonstrated that the proposed computational approach is robust and provides accurate results. Copyright © 2011 John Wiley & Sons, Ltd.     

Stochastic finite element method for elasto‐plastic body

This paper proposes a Stochastic Finite Element Method (SFEM) for non‐linear elasto‐plastic bodies, as a generalization of the SFEM for linear elastic bodies developed by Ghanem and Spanos who applied the Karhunen–Loeve expansion and the polynomial chaos expansion for stochastic material properties and field variables, respectively. The key feature of the proposed SFEM is the introduction of two fictitious bodies whose behaviours provide upper and lower bounds for the mean of field variables. The two bounding bodies are rigorously obtained from a given distribution of material properties. The deformation of an ideal elasto‐plastic body of the Huber–von Mises type is computed as an illustrative example. The results are compared with Monte‐Carlo simulation. It is shown that the proposed SFEM can satisfactorily estimate means, variances and other probabilistic characteristics of field variables even when the body has a larger variance of the material properties. Copyright © 1999 John Wiley & Sons, Ltd.     

Periodic Galerkin finite element method of tidal flow

This paper presents the finite element method of the analysis of tidal flow. Assuming that tidal flow is periodic, the Galerkin approach is employed as the numerical integration procedure in time using a trigonometric function as the interpolation function. The present method has shown to be suitable for computation especially from the point of computing time and numerical stability.     

压力型雾化等径喷嘴流场特性的有限元模拟

基于有限元液体连续相湍流仿真模型,研究柴油机用等径喷嘴内部油液的流动情况,分析入口压力对气相体积分数、湍动能和对称轴线速度的影响。结果表明:压力下降明显发生在喷嘴入口处,喷孔入口处靠近孔壁位置的湍流能最大,油液的轴向移动速度和承受的压强成反比;随着入口压力的增大,气相体积分数呈单调增加的趋势,当入口压力增大到120 MPa后,气相体积分数稳定在100%;湍动能最大处的位置由开始的喷孔入口中心轴处逐渐转移到喷嘴入口壁面上,入口压力与流速近似于呈线性变化规律;综合分析确定入口压力在100~120 MPa对保障压力型等径喷嘴燃油雾化效率是较为有利的。     

The application of the formability utilization indicator for finite element modeling the ductile fracture during the material blanking process

The purpose of researches presented in the paper was to achieve the numerical model of material blanking process for engineering purposes. The beginning and course of the ductile fracture phase has been modeled using so called “formability utilization indicator”. For this reason, the specialized subroutine for MSC MARC/Mentat software has been developed and implemented to calculate the formability utilization indicator, which functions also as a ductile fracture criterion. The original experimental and numerical methodology to determine the formability limit function has been developed. This methodology enables determining the function course based on the tension test and shearing of the original plane specimen with notch. FEM simulation for blanking has been performed for specimens made of sheet steel S355JR (thickness 3.5 mm) for clearance Lj = 0.5 mm and 0.05 mm. The fracture progress has been modeled by step-by-step deleting the segments, where the formability utilization indicator’s critical value has been exceeded. The results of modeling have been compared with experimental results, in particular attention to the cross-cut section shape.     

A1 超声塑焊变幅器的有限元分析

本文根据有限元原理自编了ＭＶＵＨ程序，可以在微机上运行，并对超声塑料焊接用的变幅器（焊头）进行分析计算，比较了平板变幅器开槽前后以及槽宽对固有频率及变幅器工作端面位移振幅分布的影响，表明开槽后变幅器的固有频率下降，位移分布较均匀，而槽加宽时固有频率略有下降。为检验程序的正确性，曾用ＡＤＩＮＡ程序包进行计算比较，得到较满意的结果，并对固有频率进行实验验证，理论计算和测量结果符合较好。     

A study of crack-tip plastic zone by elastoplastic finite element analysis

An elastoplastic finite element analysis has been carried out on a thin centre cracked panel using plane eight noded quadratic quadrilateral isoparametric elements with nonsingular displacement formulation. The linearised total strain method has been employed for the solution and the material data including those pertaining to postyield behaviour were used for the evaluation of the crack-tip stress field. The shape and size of the plastic zones at the crack tip corresponding to four stress levels have been obtained, which compare favourably with those obtained by other researchers.     

The extended finite element method for rigid particles in Stokes flow

A new method for the simulation of particulate flows, based on the extended finite element method (X‐FEM), is described. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The near field form of the fluid flow about each particle is built into the finite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive generation of hexahedral element meshes for finite element analysis of metal plastic forming process

A method for the adaptive generation of hexahedral element mesh based on the geometric features of solid model is proposed. The first step is to construct the refinement information fields of source points and the corresponding ones of elements according to the surface curvature of the analyzed solid model. A thickness refinement criterion is then used to construct the thickness-based refinement information field of elements from digital topology. The second step is to generate a core mesh through removing all the undesired elements using even and odd parity rules. Then the core mesh is magnified in an inside–out manner method through a surface node projection process using the closest position approach. Finally, in order to match the mesh to the characteristic boundary of the solid model, a threading method is proposed and applied. The present method was applied in the mesh construction of different engineering problems. The resulting meshes are well-shaped and capture all the geometric features of the original solid models.     

有限元简化模型应用于超声换能器模拟分析

依据有限元方法的基本物理思想,在某些不需要计算辐射声场的准确声学参数和波束特性的工程应用方面,对流体模型进行充分简化,提出了简化模型处理的有效方法,利用该方法对超声换能器进行模拟分析,并进行了样品的制作和测试,实测结果与模型简化分析处理的结果基本一致。可以证明,用该方法进行换能器的优化设计是可行和高效的。