Use Of Finite Elements Research Articles

Evolution of anisotropy of sheet metals during plastic deformation

Sheet metals generally exhibit a considerable anisotropy due to their crystallographic texture. The mechanical anisotropic characteristics of the sheet metal have a great influence on the shape of the specimen after the deformation. Therefore many successful phenomenological models have been proposed for use in Finite Ele-ment (FE) codes to simulate the anisotropic behavior of a material. The anisotropy is mainly described on the basis of the initial Lankford coefficients and/or yield stresses along the orthotropic (rolling and transverse) and diagonal axes of the sheet metals. The different yield functions make use of different combinations of these constant parameters to represent a 3-dimensional surface (in case of plane stress) determining the transition between elastic and plastic deformation. Generally, the evolution of anisotropy is not considered in the formulation of a constitutive model. Therefore we studied the effects of plastic work on the evolution of anisotropic behavior. The experiments consist of conventional tensile testing of specimens taken at different orientations with respect to the rolling direction. Strain measurements are performed by means of an optical measurement technique. A simple (but powerful) technique for considering distortional anisotropy applicable to any yield criterion is presented. This technique is based on the polynomial definition for instantaneous Lankford coefficient combined with Newton-Raphson iteration. The same approach is applied for evolution of yield stress.

The use of finite-element based programs in the study of atmospheric phenomena

The academic problem described in this paper concerns the measures to protect an idealized building against atmospheric discharges. The proposed lightning protection system contains a Franklin rod and two down conductors connected to the ground. The problem is analyzed computationally employing a two-dimensional finite element program. Two numerical models are used to investigate the distributions of electric potential and electric field around the building. Numerical results show that, by using the proposed lightning protection system, the mean value of the electric field close to the building increases more than four times. The paper also presents a theoretical description on fair-weather and storm conditions.

Exploration versus exploitation using kriging surrogate modelling in electromagnetic design

PurposeDesign optimisation of electromagnetic devices is computationally expensive as use of finite element or similar codes is normally required. Thus, one of the objectives is to have efficient algorithms minimising the number of necessary function calls. In such algorithms a balance between exploration and exploitation needs to be found not to miss the global optimum but at the same time to make efficient use of information already found. The purpose of this paper is a contribute to the search of such efficient algorithms.Design/methodology/approachThis paper discusses the use of kriging surrogate modelling in multiobjective design optimisation in electromagnetics. The investigation relies on the use of special test functions.FindingsThe importance of achieving appropriate balance between exploration and exploitation is emphasised when searching for the global optimum. New strategies are proposed using kriging.Originality/valueIt is argued that the proposed approach will yield a procedure to solve time consuming electromagnetic design problems efficiently and will also assist the decision making process to achieve a robust design of practical devices considering tolerances and uncertainties.

Influence of deposited metal structures on the failure mechanisms of silicon-based components

Miniaturised silicon-based multilayer chips are nowadays widespread as semiconductor components for the mobile device technology. The use of special processing and integration procedures requires such materials to possess a definite mechanical strength to ensure the functionality of the entire device. The strength and mechanical reliability of such components can be described by the Weibull theory, and is highly influenced by the geometry of the metallisation and other near-surface functional layers. In this work, we attempt to clarify the mechanisms leading to the failure of the metallised side of Si-chip components. The combined use of Finite Elements (FE) and Focused Ion Beam (FIB) analyses allowed recognising that cracks are induced in the metal-oxide-silicon interfacial area well before complete failure of the component. Such cracks have a crucial role in the lower strength and higher Weibull modulus observed on the metallised side.

Use of Finite Element and Finite Segment Methods in Modeling Rail Flexibility: A Comparative Study

Safety requirements and optimal performance of railroad vehicle systems require the use of multibody system (MBS) dynamics formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. The first method is based on the floating frame of reference (FFR) formulation which allows for the use of a detailed finite element mesh with the component mode synthesis technique in order to obtain a reduced order model. In the second method, the flexible body is modeled as a finite number of rigid elements that are connected by springs and dampers. This method, called finite segment method (FSM) or rigid finite element method, requires the use of rigid MBS formulations only. In the third method, the FFR formulation is used to obtain a model that is equivalent to the FSM model by assuming that the rail segments are very stiff, thereby allowing the exclusion of the high frequency modes associated with the rail deformations. This FFR/FS model demonstrates that some rail movement scenarios such as gauge widening can be captured using the finite element FFR formulation. The three procedures FFR, FSM, and FFR/FS will be compared in order to establish differences among them and analyze the specific application of the FSM to modeling track flexibility. Convergence of the methods is analyzed. The three methods proposed in this investigation for modeling the movement of three-dimensional tracks are used with a three-dimensional elastic wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail deformations. Several conclusions will be drawn in view of the results obtained in this investigation.

Numerical damping of spurious oscillations: a comparison between the bulk viscosity method and the explicit dissipative Tchamwa–Wielgosz scheme

The use of Finite Element and Finite Difference methods of spatial and temporal discretization for solving structural dynamics problems gives rise to purely numerical errors. Among the many numerical methods used to damp out the spurious oscillations occurring in the high frequency domain, it is proposed here to analyse and compare the Bulk Viscosity method, which involves calculating the stresses, and a method recently presented by Tchamwa and Wielgosz, which is based on an explicit time integration algorithm. The 1-D study and the 2-D axisymmetric study on a bar subjected to compression and impact loads presented here show that the former method is insensitive to meshing irregularities, whereas the latter method is not. The Bulk Viscosity method was found to be sensitive, however, to the behavior of the material, contrary to the Tchamwa---Wielgosz method. Since comparisons of this kind are rather complex, a specific method of analysis was developed.

Ultimate collapse strength assessment of damaged steel-plated structures

In an unpredictable world where human intervention or unexpected environmental conditions can prevail, damage can occur to manmade structures. Whilst structural design allows for redundancy, or a structural capability beyond the general working load of the structure, it is necessary to be able to analyse and understand the residual capability of a damaged structure to ensure the safety of personnel in the vicinity of the structure and assess the potential to facilitate repair.Idealised Structural Unit Method (ISUM) can allow rapid assessment of large structural arrangements by simplification into smaller constituent parts, which are assessed against pre-calculated failure data for each part. The method has potential benefits for allowing rapid assessment of damaged steel-plated structure that would otherwise require the use of high fidelity modelling of the entire structures, such as through the use of finite element analysis.This paper presents a study on the use of ISUM to assess damaged steel-plated structures and its limitations through the collapse analysis of stiffened steel panels. A new ISUM is proposed for strength assessment of damaged structural arrangements. Analysis is undertaken to assess the effects of geometrical and material property variations that can occur in a structure as well as the effects of damage aperture size and shape on the collapse strength of stiffened steel panels. The study shows that while ISUM can be applied in the assessment of damaged steel-plated structures, implementing the proposed new ISUM allows greater accuracy in the calculation of the collapse strength of damaged stiffened steel panels. The paper also concludes that the assessment of larger structural units for application in the ISUM assessment, will allow the effects of the damage on surrounding structure to be captured, which can influence the deflection shapes that will lead to collapse of the structure.

Interaction analysis and optimal design of composite action of plastered straw bale

PurposeThe purpose of this paper is to assess the effects of cement‐ and earth‐plastered straw bale walls against the appropriate vertical loads.Design/methodology/approachThe effects of contact between two common types of plasters and the stacked straw bale by the optimal design analysis have been assessed in this work with the use of finite element method.FindingsCement‐ and earth‐plastered straw bale walls have shown adequate resistance against the appropriate vertical loads and showed that the earth‐plaster can bear higher stress than the cement plastered straw bale. There is the implication that the collapse or response of the earth‐straw bale wall will be significantly higher compared to that of cement‐straw bale wall.Practical implicationsThe stress stability obtained of the analytical walls is adequate after using the best fit variables for the wall height and thickness.Originality/valueThe paper shows that the allowable stresses of 70.14 kN/m2 for cement plastered straw bale wall and 73.14 kN/m2 for earth‐plastered straw bale wall are higher than the calculated stress values using SAP2000 of 18.836 and 64.2 kN/m2 for cement plastered straw bale wall, respectively.

Modeling of reinforced concrete through SPH‐FE coupling and its application to the simulation of a projectile's impact onto a slab

AbstractThe analysis of structural behavior under extreme solicitations such as crash and impact requires the modeling of fragmentation, rupture and large deformation phenomena. The use of finite elements (FE) in this type of problem is not easy, mainly because this approach relies on a mesh that cannot handle distortions and tearing well. In order to circumvent this difficulty, methods termed ‘meshless’, such as the smoothed particle hydrodynamics (SPH) method, have been devised. These methods enable one to undertake numerical simulations involving the extreme types of behavior mentioned above. Thus, for example, the simulation of a projectile's impact onto a reinforced concrete slab can be easily envisaged. One's wish to carry out predictive calculations raises the question of the modeling of the reinforcement. It is tempting to use an SPH formulation for the slab and a beam FE formulation for the reinforcement. Therefore, the problem boils down to the coupling of two structures modeled with two different formulations: the slab with an SPH formulation, and the reinforcement with a FE formulation. This paper presents the development of a theory based on the use of Lagrange multipliers, which enable the coupling of a structure modeled with SPH with a structure modeled with beam FEs. This theory was implemented into the EUROPLEXUS fast dynamics software, then validated through simple test cases. Finally, the program was applied to the simulation of a projectile's impact onto a reinforced concrete slab.The aim of this work is to propose an alternative method to smeared representations of reinforcements in concrete. Indeed, smeared representations of reinforced concrete are widely used but do not represent explicitly the reinforcement, which is fundamental to study impacts onto the rebars and phenomenons such as separation of the reinforcement from the concrete or fracture of the rebars. Copyright © 2009 John Wiley & Sons, Ltd.

A multi-body systems approach to simulate helicopter occupant protection systems

This paper reports on the work of computer simulations carried out at Coventry University as part of the European 6th Framework HeliSafe TA project, which considered the potential improvements in occupant safety for civil helicopters. A multi-body systems approach with additional use of finite elements for critical components such as a pilot airbag and the harnesses was adopted in the computer models to simulate helicopter crash/rollover scenarios and to investigate the effectiveness of occupant protection systems deployed during helicopter crash scenarios. ADAMS and Madymo simulations of helicopter impact/rollover events were demonstrated. A cabin/cockpit model of a Bell UH-1D helicopter was developed to replicate the physical crash test setup and a parametric study for the pilot airbag and a range of harness concepts was performed. The use of validated multi-body systems-based cabin/cockpit models has proved to be effective in the development of new restraint system concepts for occupant protection.

Applications of numerical methods in biomechanics

Numerical methods are used in biomechanics like many other branches of engineering. In this study some examples from literature for the use of finite element and finite volume methods have been presented. The literature survey was kept broad in order to cover a wide range of examples. The most common numerical methods used in biomechanics applications are finite element and finite volume methods therefore some examples of these applications are presented as follows: Finite element method : Development of 3D finite element models (FEM) of femurs representing their behaviour before and after the application of hip prostheses; determination of the stresses occurring at joint discs under 3D static forces; 3D FEA of lower jaw joint; estimation of design parameters of an implant used for acetabular joints by means of nonlinear FEA; the FEA of the wear and heating mechanisms involved with the metal implants used in hip joints; development of FE model for the C4–C5 segment of vertebrae that form the spinal cord and the analysis of the injuries that occur when subjected to an impact; determination of the endurance level of vertebra with defects by means of computerized tomography and FEA; comparison of test and nonlinear FEA results for the lumbar vertebrae (L12) under compression; the simulation of the biomechanical reaction shown by the lumbosacral spinal unit (L1–S1) under physiological forces and boundary conditions; the simulation of the deformation occurring in the brain during a craniotomic surgery; FEA of cornea; FE simulation of the laceration of the cornea for astigmatism treatment; investigation of the biomechanical response of dental implants and the skeletal system in the vicinity under the influence of static and harmonic forces by means of FEA; life analysis of ceramic coatings on teeth under cyclic occlusion forces; ballistic simulation of a bullet penetrating the lower jaw of a boar and other similar studies were given. Finite volume method : Studies such as the calculation of the hydrodynamic forces for an arm without a hand; the computational fluid dynamics (CFD) analysis of the blood flowing in the vertebral arteries; enhancement of stent designs via CFD simulations; development of 3D CFD models of stents placed to coroner artery and investigation of the irregularities caused in the flow of blood for four different stent designs; investigation of aerosol deposition in lungs due to respiration, etc. were given. In this study some examples of FEM and CFD in biomechanics were given as applications of numerical methods in this field. It was observed that in these studies the models used were usually generated from BT and MR images. Also the analyses were generally accompanied by experimental studies for verification. In this compiling study examples of the application of numerical methods in the field of biomechanics were taken from the literature. The analyses were usually tried to be verified with experiments so as to set examples for further studies. By means of the use of numerical methods in biomechanics that is recently becoming more important, many illnesses may be investigated and new treatment methods may be developed.

Fast and accurate point-based method for time-harmonic maxwell problems involving thin layer materials

We present a high-order hybrid boundary-finite elements method well-suited for solving time-harmonic electromagnetic scattering problems. Actually, this method is specially devoted to perfect electric conductors coated with a thin layer material. On such class of problems this method is shown to be fast and accurate. The fast feature is due to the joint use of finite elements of anisotropic order fitting the layer thickness, and of a point-based boundary element method on the skin. The accuracy is ensured, first by a discretization scheme satisfying the H curl– H div conformity required by the integro-differential equation and, secondly, by an adaptive technique of integration based on the detection of some local potential trouble on the geometry such as sharp edges or high dilatation of the elements. This algorithm does not need further information from the user and does not deteriorate the computation time. Numerical examples confirm the efficiency of this approach.

Concurrent use of finite element and finite volume methods for shallow water flows in locally 1-D channel networks

SUMMARY A numerical model is developed for shallow water equation in locally 1-D channel networks. The model concurrently uses the standard Galerkin finite element method for the continuity equation and the finite volume method with an upwind scheme for the momentum equation. The surface gradient method is consistently employed. A minimum treatment is given for channel junctions so that application to multiply connected channels do not require any special consideration The model is capable of computing different types of transcritical flows, wet and dry flows, and flows with complex source terms. Standardized test problems and laboratory experimental data are used for verifying the model. Applicability of the models is validated in a multiply connected channel network draining hydromorphic farmlands located in a West African savanna, and Manning's roughness coefficient is identified, so that the steady solution is consistent with field observations. Unsteady simulation demonstrates that the model is capable of stably reproducing shifts of hydraulic jumps in flows of sub-millimeter water depths. Copyright © 2011 John Wiley & Sons, Ltd.

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

On the use of some numerical damping methods of spurious oscillations in the case of elastic wave propagation

The use of finite element and finite difference methods of spatial and temporal discretization for solving structural dynamics problems gives rise to purely numerical errors. Among the many numerical methods used to damp out the spurious oscillations occurring in the high frequency domain, it is proposed here to analyse and compare the well-known Bulk Viscosity method, which modifies the stresses calculations and a method recently presented by Tchamwa and Wielgosz, which is based on a modification of an explicit time integration algorithm. The efficiency of both methods is evaluated in a 2-D axisymmetric compressive test.

Extended 2D magnetic equivalent circuit method

PurposeThe purpose of this paper is to devise a magnetic field modelling approach suitable for simulating the transient behaviour of a class of electromagnetic systems (particularly linear synchronous motors).Design/methodology/approachThe classical 2D magnetic equivalent circuit (MEC) approach is extended by separately accounting for leakage flux from highly permeable polygonal regions (where the MEC approach is most applicable). It capitalises on the computational efficiency of an MEC approach for regions where the flux can be assumed to be uniformly channelled through a coarse network of “flux tubes” and accounts for leakage flux from these regions by introducing mutual permeances. These mutual permeances are geometry dependent and can be calculated upfront using a surface‐current representation of the magnetomotive force attributed to each flux tube.FindingsAs demonstrated with a simple example, the magnetic field solution converges with an increasing subdivision of flux tubes, yielding a transparent trade‐off between simulation time and accuracy.Research limitations/implicationsUsing Schwarz‐Christoffel mapping to approximate the mutual permeances is restrictive and introduces unnecessary error. Hence, the use of finite element or boundary element methods to obtain these permeances is under investigation. Furthermore, it is expected that introducing 2D flux tube elements for junction regions would be beneficial.Originality/valueA novel approach is presented that aims to improve the accuracy of a traditional MEC solution, whilst retaining its computational advantage for the flux that is well channelled. The method has particular merit for the dynamic modelling of linear motors, where the machine's behaviour is dominated by the flux bridging the air gap.

The natural frequencies of muted circular drums.

The natural frequencies of circular drum heads are calculated by the use of finite elements. The results for unmuted drum heads are almost identical to the well known analytical solution expressed in Bessel functions. Mutes of various sizes and shapes are used to stop a section of the head from vibrating. For example, a circular damper having one-quarter of the drum head diameter raises the resonant frequencies of the first eight modes of vibration by 11%, 1.7%, 15.1%, 3.8%, 6.2%, 9.2%, 5.2%, and 10.1%. For the undamped drum head, modes two and three are identical. Modes four and five are identical as well as modes seven and eight. Each of the pairs have differing resonant frequencies. The changes in resonant frequencies are strongly influenced by where the mute is placed. It would seem that the calculated frequency changes could be used to musical advantage.

Effect of training algorithms on neural networks aided pavement diagnosis

Routine pavement maintenance necessitates present structural diagnosis and condition evaluation of pavements by employing non-destructive test equipment such as the Falling Weight Deflectometer (FWD). FWD testing of pavements involves measuring time-domain surface deflections resulting from applied impulse loading on the pavement. Through inverse analysis of FWD deflection data, the stiffness parameters of the individual pavement layers are, in general, determined using iterative optimization routines. In recent years, Neural Networks (NN) aided inverse analysis has emerged as a successful alternative for predicting pavement layer moduli from FWD deflection data in real-time. Especially, the use of Finite Element (FE) based pavement modeling results for training the NN aided inverse analysis is considered to be accurate in realistically characterizing the non-linear stress-sensitive response of underlying pavement layers in real-time. Efficient NN learning algorithms have been developed and proposed to determine the weights of the network, according to the data of the computational task to be performed. In this paper, the effect of training algorithms on the NN aided inversion process is analyzed and discussed. Keywords: Neural networks; Non-destructive testing; Inverse analysis; Finite element; Flexible pavement.

Observations on Limit Equilibrium–Based Slope Reliability Problems with Inclined Weak Seams

This study addresses the complexity of slope reliability problems based on limit equilibrium methods (LEMs). The main focus is on the existence of multiple failure modes that poses difficulty to many LEM-based slope reliability methods. In particular, when weak seams are present, the failure modes associated with those seams may be difficult to detect. A systematic way of searching the failure modes is proposed, and its robustness over slopes with or without weak seams is demonstrated. It is found that in the presence of weak seams, assuming circular slip surfaces may cause underestimation of slope failure probability. The conclusion of the study promotes the use of finite elements as the stability method for reliability evaluation because it is not necessary to search for failure surfaces in finite-element stability analysis.

Structural Analysis of Composite Shield Cutter-Head and Cutters Arrangement Optimization Based on Finite Element

With the comprehensive use of finite element and computer simulation, the cutter-head was analyzed and optimized. Based on the full analysis of structural features of the cutter-head, the finite element analysis model of the cutter-head was set up by using Solidworks and ANSYS. The analyses of the cutter-head under two kinds of limit load conditions were carried out and the stress distribution of the cutter-head was obtained. According to the tunneling characteristics, the cutters were re-arranged. The analysis showed that under the same conditions, the stress distribution of the improved structure was more symmetrical and the maximum stress and maximum deformation also had a remarkable reduction. Also there was a greater stress between the corbel and the flange; it would be of vital significance to increase the welding strength of these parts. And the results could provide basic data for the structure design of cutter-head.