A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Finite element modelling of metallic tubular crash structures with an explicit code

Numerous experimental studies have been carried out to investigate the collapse of tubular metallic crash structures under axial compression. Some simple theoretical models have been developed but these often assume one type of progressive collapse, which is not always representative of the real situation. Finite Element (FE) models, when further refined, have the potential to predict the actual collapse mode and how it influences the load-displacement and energy absorption characteristics. This paper describes an FE modelling investigation with the explicit code LS−DYNA. An automatic mesh generation programme written by the authors is used to set up shell and solid element tube models. Mesh specification issues and features relating to the contact and friction models are discussed in detail. The crush modes, load-deflection characteristics and energy absorption values found in the simulations are compared with a reasonable degree of correlation to those observed in a physical testing programme; however, improvements are still required.

Experimental investigation and finite element analysis for the study of residual stresses in roller burnished components

Burnishing is a surface modification process, which involves plastic deformation of the material at the surface of the component due to the application a highly polished and hard roller, under pressure. This results in the improvement of the surface finish of the component and induces residual compressive stresses on the surface of the component. The present work deals with the optimization of the burnishing force for the best surface finish, at constant speed and feed, for Aluminium and Mild steel workpieces. A 3dimensional finite element model is proposed for the simulation of the burnishing process, and the analysis is carried out at the optimum force determined experimentally. The induced compressive stress in the components is determined from the finite element analysis and this value is then compared with the results obtained from X-ray diffraction technique.

Prediction of residual stresses in roller burnished components : a finite element approach

Surface finish is an important factor in creating the durable metal components, and fatigue strength can be improved if compressive residual stresses are produced in the surface. Burnishing is a finishing process and compressive residual stresses are induced during the process. The present study of minimizing the surface roughness based on the experimental work, and finite element model was developed to evaluate the analytical results. Commercial purity Mild Steel and Aluminium were selected as work specimens and a high carbon high chromium roller was used as a tool for the burnishing process.

Contact pressure prediction in sheet metal forming using finite element analysis

Tool wear has become a significant issue associated with the forming of high strength sheet steels in the automotive industry. In order to combat this problem, recent research has been devoted to utilizing the contact results obtained from current sheet metal forming software predictions, in order to develop/apply tool wear models or tool material selection criteria for use in the stamping plant. This investigation aims to determine whether a specialized sheet metal forming software package can correctly capture the complex contact conditions that occur during a typical sheet metal stamping process. The contact pressure at the die radius was compared to results obtained using a general-purpose finite element software package, for a simple channel-forming process. Although some qualitative similarities between the two predictions were observed, it was found that significant differences in the magnitude and distribution of the contact pressure exists. The reasons for the discrepancies in results are discussed with respect to the simplifications and assumptions adopted in the finite element model definitions, and with regards to other results available in the literature.

Finite element modeling of a generic stemless hip implant design in comparison with conventional hip implants

In this study, the finite element modeling and comparison of the stress and strain analyses were carried out for three different structures that are intact bone, stemless implant and stemmed one. Currently proposed stemless design studied here is the generic concept of stemless implant. This generic stemless implant reconstruction was numerically compared to the conventional stemmed implant and also to the intact bone as control solution. Two loading conditions were applied to the most proximal part of the models, while the most distal part was fixed for all degrees of freedom. The models were divided into two regions and studied along two paths of medial and lateral aspect. The results of this study showed that the stemless implant had less deviation from the control solution of the bone in all regions and in both loading conditions, comparing to the large deviation of the stemmed implant from the intact bone. However, it was shown that the fixation of this type of implant and its effect on sub-trochanter region must be carefully considered for designing the final product of any specific design of stemless implant.