A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

System identification of linear vibrating structures

Methods of dynamic modelling and analysis of structures, for example the finite element method, are well developed. However, it is generally agreed that accurate modelling of complex structures is difficult and for critical applications it is necessary to validate or update the theoretical models using data measured from actual structures. The techniques of identifying the parameters of linear dynamic models using Vibration test data have attracted considerable interest recently. However, no method has received a general acceptance due to a number of difficulties. These difficulties are mainly due to (i) Incomplete number of Vibration modes that can be excited and measured, (ii) Incomplete number of coordinates that can be measured, (iii) Inaccuracy in the experimental data (iv) Inaccuracy in the model structure. This thesis reports on a new approach to update the parameters of a finite element model as well as a lumped parameter model with a diagonal mass matrix. The structure and its theoretical model are equally perturbed by adding mass or stiffness and the incomplete number of eigen-data is measured. The parameters are then identified by an iterative updating of the initial estimates, by sensitivity analysis, using eigenvalues or both eigenvalues and eigenvectors of the structure before and after perturbation. It is shown that with a suitable choice of the perturbing coordinates exact parameters can be identified if the data and the model structure are exact. The theoretical basis of the technique is presented. To cope with measurement errors and possible inaccuracies in the model structure, a well known Bayesian approach is used to minimize the least squares difference between the updated and the initial parameters. The eigen-data of the structure with added mass or stiffness is also determined using the frequency response data of the unmodified structure by a structural modification technique. Thus, mass or stiffness do not have to be added physically. The mass-stiffness addition technique is demonstrated by simulation examples and Laboratory experiments on beams and an H-frame.

Parametric study of the behaviour of reinforced concrete columns in fire

The research is concerned with the application of the computer simulation technique to study the performance of reinforced concrete columns in a fire environment. The effect of three different concrete constitutive models incorporated in the computer simulation on the structural response of reinforced concrete columns exposed to fire is investigated. The material models differed mainly in respect to the formulation of the mechanical properties of concrete. The results from the simulation have clearly illustrated that a more realistic response of a reinforced concrete column exposed to fire is given by a constitutive model with transient creep or appropriate strain effect The assessment of the relative effect of the three concrete material models is considered from the analysis by adopting the approach of a parametric study, carried out using the results from a series of analyses on columns heated on three sides which produce substantial thermal gradients. Three different loading conditions were used on the column; axial loading and eccentric loading both to induce moments in the same sense and opposite sense to those induced by the thermal gradient. An axially loaded column heated on four sides was also considered. The computer modelling technique adopted separated the thermal and structural responses into two distinct computer programs. A finite element heat transfer analysis was used to determine the thermal response of the reinforced concrete columns when exposed to the ISO 834 furnace environment. The temperature distribution histories obtained were then used in conjunction with a structural response program. The effect of the occurrence of spalling on the structural behaviour of reinforced concrete column is also investigated. There is general recognition of the potential problems of spalling but no real investigation into what effect spalling has on the fire resistance of reinforced concrete members. In an attempt to address the situation, a method has been developed to model concrete columns exposed to fire which incorporates the effect of spalling. A total of 224 computer simulations were undertaken by varying the amounts of concrete lost during a specified period of exposure to fire. An array of six percentages of spalling were chosen for one range of simulation while a two stage progressive spalling regime was used for a second range. The quantification of the reduction in fire resistance of the columns against the amount of spalling, heating and loading patterns, and the time at which the concrete spalls appears to indicate that it is the amount of spalling which is the most significant variable in the reduction of fire resistance.

The application of contact mechanics to the numerical simulation of particulate material

Particulate solids are complex redundant systems which consist of discrete particles. The interactions between the particles are complex and have been the subject of many theoretical and experimental investigations. Invetigations of particulate material have been restricted by the lack of quantitative information on the mechanisms occurring within an assembly. Laboratory experimentation is limited as information on the internal behaviour can only be inferred from measurements on the assembly boundary, or the use of intrusive measuring devices. In addition comparisons between test data are uncertain due to the difficulty in reproducing exact replicas of physical systems. Nevertheless, theoretical and technological advances require more detailed material information. However, numerical simulation affords access to information on every particle and hence the micro-mechanical behaviour within an assembly, and can replicate desired systems. To use a computer program to numerically simulate material behaviour accurately it is necessary to incorporte realistic interaction laws. This research programme used the finite difference simulation program `BALL', developed by Cundall (1971), which employed linear spring force-displacement laws. It was thus necessary to incorporate more realistic interaction laws. Therefore, this research programme was primarily concerned with the implementation of the normal force-displacement law of Hertz (1882) and the tangential force-displacement laws of Mindlin and Deresiewicz (1953). Within this thesis the contact mechanics theories employed in the program are developed and the adaptations which were necessary to incorporate these laws are detailed. Verification of the new contact force-displacement laws was achieved by simulating a quasi-static oblique contact and single particle oblique impact. Applications of the program to the simulation of large assemblies of particles is given, and the problems in undertaking quasi-static shear tests along with the results from two successful shear tests are described.

Temporal finite elements in the dynamic analysis of structures

This thesis demonstrates that the use of finite elements need not be confined to space alone, but that they may also be used in the time domain, It is shown that finite element methods may be used successfully to obtain the response of systems to applied forces, including, for example, the accelerations in a tall structure subjected to an earthquake shock. It is further demonstrated that at least one of these methods may be considered to be a practical alternative to more usual methods of solution. A detailed investigation of the accuracy and stability of finite element solutions is included, and methods of applications to both single- and multi-degree of freedom systems are described. Solutions using two different temporal finite elements are compared with those obtained by conventional methods, and a comparison of computation times for the different methods is given. The application of finite element methods to distributed systems is described, using both separate discretizations in space and time, and a combined space-time discretization. The inclusion of both viscous and hysteretic damping is shown to add little to the difficulty of the solution. Temporal finite elements are also seen to be of considerable interest when applied to non-linear systems, both when the system parameters are time-dependent and also when they are functions of displacement. Solutions are given for many different examples, and the computer programs used for the finite element methods are included in an Appendix.

Kineto-elastodynamic analysis of high-speed four-bar mechanism

This thesis addresses the kineto-elastodynamic analysis of a four-bar mechanism running at high-speed where all links are assumed to be flexible. First, the mechanism, at static configurations, is considered as structure. Two methods are used to model the system, namely the finite element method (FEM) and the dynamic stiffness method. The natural frequencies and mode shapes at different positions from both methods are calculated and compared. The FEM is used to model the mechanism running at high-speed. The governing equations of motion are derived using Hamilton's principle. The equations obtained are a set of stiff ordinary differential equations with periodic coefficients. A model is developed whereby the FEM and the dynamic stiffness method are used conjointly to provide high-precision results with only one element per link. The principal concern of the mechanism designer is the behaviour of the mechanism at steady-state. Few algorithms have been developed to deliver the steady-state solution without resorting to costly time marching simulation. In this study two algorithms are developed to overcome the limitations of the existing algorithms. The superiority of the new algorithms is demonstrated. The notion of critical speeds is clarified and a distinction is drawn between "critical speeds", where stresses are at a local maximum, and "unstable bands" where the mechanism deflections will grow boundlessly. Floquet theory is used to assess the stability of the system. A simple method to locate the critical speeds is derived. It is shown that the critical speeds of the mechanism coincide with the local maxima of the eigenvalues of the transition matrix with respect to the rotational speed of the mechanism.

Pattern competition in volumetricaly heated fluids

Finite element simulations have been performed along side Galerkin-type calculations that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Prediction of welding distortion in butt joint of thin plates

This paper investigates distortions and residual stresses induced in butt joint of thin plates using Metal Inert Gas welding. A moving distributed heat source model based on Goldak's double-ellipsoid heat flux distribution is implemented in Finite Element (FE) simulation of the welding process. Thermo-elastic-plastic FE methods are applied to modelling thermal and mechanical behaviour of the welded plate during the welding process. Prediction of temperature variations, fusion zone and heat affected zone as well as longitudinal and transverse shrinkage, angular distortion, and residual stress is obtained. FE analysis results of welding distortions are compared with existing experimental and empirical predictions. The welding speed and plate thickness are shown to have considerable effects on welding distortions and residual stresses. © 2009 Elsevier Ltd. All rights reserved.

Interpretation of the Superpave IDT strength test using a viscoelastic-damage constitutive model

This paper presents a new interpretation for the Superpave IDT strength test based on a viscoelastic-damage framework. The framework is based on continuum damage mechanics and the thermodynamics of irreversible processes with an anisotropic damage representation. The new approach introduces considerations for the viscoelastic effects and the damage accumulation that accompanies the fracture process in the interpretation of the Superpave IDT strength test for the identification of the Dissipated Creep Strain Energy (DCSE) limit from the test result. The viscoelastic model is implemented in a Finite Element Method (FEM) program for the simulation of the Superpave IDT strength test. The DCSE values obtained using the new approach is compared with the values obtained using the conventional approach to evaluate the validity of the assumptions made in the conventional interpretation of the test results. The result shows that the conventional approach over-estimates the DCSE value with increasing estimation error at higher deformation rates.

Design and analysis of a 2-DoF split-stator induction motor

A two degrees of freedom (2-DOF) actuator capable of producing linear translation, rotary motion, or helical motion would be a desirable asset to the fields of machine tools, robotics, and various apparatuses. In this paper, a novel 2-DOF split-stator induction motor was proposed and electromagnetic structure pa- rameters of the motor were designed and optimized. The feature of the direct-drive 2-DOF induction motor lies in its solid mover ar- rangement. In order to study the complex distribution of the eddy current field on the ferromagnetic cylinder mover and the motor’s operating characteristics, the mathematical model of the proposed motor was established, and characteristics of the motor were ana- lyzed by adopting the permeation depth method (PDM) and finite element method (FEM). The analytical and numerical results from motor simulation clearly show a correlation between the PDM and FEM models. This may be considered as a fair justification for the proposed machine and design tools.

In situ diagnostics and prognostics of solder fatigue in IGBT modules for electric vehicle drives

This paper proposes an in situ diagnostic and prognostic (D&P) technology to monitor the health condition of insulated gate bipolar transistors (IGBTs) used in EVs with a focus on the IGBTs' solder layer fatigue. IGBTs' thermal impedance and the junction temperature can be used as health indicators for through-life condition monitoring (CM) where the terminal characteristics are measured and the devices' internal temperature-sensitive parameters are employed as temperature sensors to estimate the junction temperature. An auxiliary power supply unit, which can be converted from the battery's 12-V dc supply, provides power to the in situ test circuits and CM data can be stored in the on-board data-logger for further offline analysis. The proposed method is experimentally validated on the developed test circuitry and also compared with finite-element thermoelectrical simulation. The test results from thermal cycling are also compared with acoustic microscope and thermal images. The developed circuitry is proved to be effective to detect solder fatigue while each IGBT in the converter can be examined sequentially during red-light stopping or services. The D&P circuitry can utilize existing on-board hardware and be embedded in the IGBT's gate drive unit.

State detection of bond wires in IGBT modules using eddy current pulsed thermography

Insulated gate bipolar transistor (IGBT) modules are important safety critical components in electrical power systems. Bond wire lift-off, a plastic deformation between wire bond and adjacent layers of a device caused by repeated power/thermal cycles, is the most common failure mechanism in IGBT modules. For the early detection and characterization of such failures, it is important to constantly detect or monitor the health state of IGBT modules, and the state of bond wires in particular. This paper introduces eddy current pulsed thermography (ECPT), a nondestructive evaluation technique, for the state detection and characterization of bond wire lift-off in IGBT modules. After the introduction of the experimental ECPT system, numerical simulation work is reported. The presented simulations are based on the 3-D electromagnetic-thermal coupling finite-element method and analyze transient temperature distribution within the bond wires. This paper illustrates the thermal patterns of bond wires using inductive heating with different wire statuses (lifted-off or well bonded) under two excitation conditions: nonuniform and uniform magnetic field excitations. Experimental results show that uniform excitation of healthy bonding wires, using a Helmholtz coil, provides the same eddy currents on each, while different eddy currents are seen on faulty wires. Both experimental and numerical results show that ECPT can be used for the detection and characterization of bond wires in power semiconductors through the analysis of the transient heating patterns of the wires. The main impact of this paper is that it is the first time electromagnetic induction thermography, so-called ECPT, has been employed on power/electronic devices. Because of its capability of contactless inspection of multiple wires in a single pass, and as such it opens a wide field of investigation in power/electronic devices for failure detection, performance characterization, and health monitoring.