Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.

Dynamic multi-partitioning for parallel finite element applications

The central product of the DRAMA (Dynamic Re-Allocation of Meshes for parallel Finite Element Applications) project is a library comprising a variety of tools for dynamic re-partitioning of unstructured Finite Element (FE) applications. The input to the DRAMA library is the computational mesh, and corresponding costs, partitioned into sub-domains. The core library functions then perform a parallel computation of a mesh re-allocation that will re-balance the costs based on the DRAMA cost model. We discuss the basic features of this cost model, which allows a general approach to load identification, modelling and imbalance minimisation. Results from crash simulations are presented which show the necessity for multi-phase/multi-constraint partitioning components

Dynamic fluid–structure interaction using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: • a single mesh covering the entire domain, • a Navier–Stokes flow, • a single FV-UM discretisation approach for both the flow and solid mechanics procedures, • an implicit predictor–corrector version of the Newmark algorithm, • a single code embedding the whole strategy.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.

Evaluation of distortions in laser welded shipbuilding parts using local-global finite element approach

In recognition of the differences of scale between the welding pool and the heat affected zone along the welding line on one hand, and the overall size of the components being welded on the other, a local-global finite element approach was developed for the evaluation of distortions in laser welded shipbuilding parts. The approach involves the tandem use of a 'local' and a 'global' step. The local step involves a three-dimensional finite element model for the simulation of the laser welding process using the Sysweld finite element code, which takes into account thermal, metallurgical, and mechanical aspects. The simulation of the laser welding process was performed using a non-linear heat transfer analysis, based on a keyhole formation model, and a coupled transient thermomechanical analysis, which takes into account metallurgical transformations using the temperature dependent material properties and the continuous cooling transformation diagram. The size and shape of the keyhole used in the local finite element analysis was evaluated using a keyhole formation model and the Physica finite volume code. The global step involves the transfer of residual plastic strains and the stiffness of the weld obtained from the local model to the global analysis, which then provides the predicted distortions for the whole part. This newly developed methodology was applied to the evaluation of global distortions due to laser welding of stiffeners on a shipbuilding part. The approach has been proved reliable in comparison with experiments and of practical industrial use in terms of computing time and storage.

Optimization and finite element analysis for reliable electronic packaging

This paper demonstrates a modeling and design approach that couples computational mechanics techniques with numerical optimisation and statistical models for virtual prototyping and testing in different application areas concerning reliability of eletronic packages. The integrated software modules provide a design engineer in the electronic manufacturing sector with fast design and process solutions by optimizing key parameters and taking into account complexity of certain operational conditions. The integrated modeling framework is obtained by coupling the multi-phsyics finite element framework - PHYSICA - with the numerical optimisation tool - VisualDOC into a fully automated design tool for solutions of electronic packaging problems. Response Surface Modeling Methodolgy and Design of Experiments statistical tools plus numerical optimisaiton techniques are demonstrated as a part of the modeling framework. Two different problems are discussed and solved using the integrated numerical FEM-Optimisation tool. First, an example of thermal management of an electronic package on a board is illustrated. Location of the device is optimized to ensure reduced junction temperature and stress in the die subject to certain cooling air profile and other heat dissipating active components. In the second example thermo-mechanical simulations of solder creep deformations are presented to predict flip-chip reliability and subsequently used to optimise the life-time of solder interconnects under thermal cycling.

Combined vertex-based - cell-centred finite volume method for flows in complex geometries

CFD modelling of 'real-life' processes often requires solutions in complex three dimensional geometries, which can often result in meshes where aspects of it are badly distorted. Cell-centred finite volume methods, typical of most commercial CFD tools, are computationally efficient, but can lead to convergence problems on meshes which feature cells with high non-orthogonal shapes. The vertex-based finite volume method handles distorted meshes with relative ease, but is computationally expensive. A combined vertex-based - cell-centred (VB-CC) technique, detailed in this paper, allows solutions on distorted meshes that defeat purely cell-centred physical models to be employed in the solution of other transported quantities. The VB-CC method is validated with benchmark solutions for thermally driven flow and turbulent flow. An early application of this hybrid technique is to three-dimensional flow over an aircraft wing, although it is planned to use it in a wide variety of processing applications in the future.

A cell-centred finite volume method for modelling viscoelastic flow

An unstructured cell-centred finite volume method for modelling viscoelastic flow is presented. The method is applied to the flow through a planar channel and the 4:1 planar contraction for creeping flow of an Oldroyd-B fluid. The results are presented for a range of Weissenberg numbers. In the case of the planar channel results are compared with analytical solutions. For the 4:1 planar contraction benchmark problem the convection terms in the constitutive equations are approximated using both first and second order differencing schemes to compare the techniques and the effect of mesh refinement on the solution is investigated. This is the first time that a fully unstructured, cell-centredfinitevolume technique has been used to model the Oldroyd-B fluid for the test cases presented in this paper.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

Micro-mechanical parameterisations for continuum modelling of granular material using the discrete element method

The present work uses the discrete element method (DEM) to describe assemblies of particulate bulk materials. Working numerical descriptions of entire processes using this scheme are infeasible because of the very large number of elements (1012 or more in a moderately sized industrial silo). However it is possible to capture much of the essential bulk mechanics through selective DEM on important regions of an assembly, thereafter using the information in continuum numerical descriptions of particulate processes. The continuum numerical model uses population balances of the various components in bulk solid mixtures. It depends on constitutive relationships for the internal transfer, creation and/or destruction of components within the mixture. In this paper we show the means of generating such relationships for two important flow phenomena – segregation whereby particles differing in some important property (often size) separate into discrete phases, and degradation, whereby particles break into sub-elements, through impact on each other or shearing. We perform DEM simulations under a range of representative conditions, extracting the important parameters for the relevant transfer, creation and/or destruction of particles in certain classes within the assembly over time. Continuum predictions of segregation and degradation using this scheme are currently being successfully validated against bulk experimental data and are beginning to be used in schemes to improve the design and operation of bulk solids process plant.