Computational Methods and Production Engineering

Research and Development

J. Paulo Davim, J Paulo Davim

• Publisher: Woodhead Publishing
• Year: 2017
• Print ISBN: 9780857094810
• eBook ISBN: 9780857094827
• Topic: Business
• Subtopic: Operations
• Index: Business

Computational Methods and Production Engineering: Research and Development is an original book publishing refereed, high quality articles with a special emphasis on research and development in production engineering and production organization for modern industry. Innovation and the relationship between computational methods and production engineering are presented.Contents include: Finite Element method (FEM) modeling/simulation; Artificial neural networks (ANNs); Genetic algorithms; Evolutionary computation; Fuzzy logic; neuro-fuzzy systems; Particle swarm optimization (PSO); Tabu search and simulation annealing; and optimization techniques for complex systems.As computational methods currently have several applications, including modeling manufacturing processes, monitoring and control, parameters optimization and computer-aided process planning, this book is an ideal resource for practitioners.- Presents cutting-edge computational methods for production engineering- Explores the relationship between applied computational methods and production engineering- Presents new innovations in the field- Edited by a key researcher in the field

1

Parallel direct solver for finite element modeling of manufacturing processes

C.V. Nielsen*; P.A.F. Martins^{† *} Technical University of Denmark, Lyngby, Denmark
^† Universidade de Lisboa, Lisbon, Portugal

Abstract

This chapter describes and evaluates the parallelization of a direct equation solver for implementation in the finite element modeling of manufacturing processes. The parallel solver is implemented in an existing three-dimensional finite element computer program for problems including large deformations, contact development, and electrical and thermal fields. Speed-up and efficiency are evaluated on a standard personal computer. Considerable time savings are achieved, allowing computations to take place in industry within reasonable computation time without access to any kind of supercomputers or clusters. The direct equation solver is parallelized for shared memory platforms by OpenMP instructions, and it can be directly implemented in existing finite element codes utilizing skyline matrix storage, no matter the physical dimensions of the problems dealt with. Only the call to the existing solver has to be substituted by a call to the proposed parallel solver. The modification of the parallel direct equation solver to be applied as preconditioner of iterative equation solvers is also discussed. The FORTRAN source code is provided in the Appendix.

Keywords

Direct solver; Parallelization; OpenMP; FEM; Numerical methods

Acknowledgments

The authors would like to acknowledge the support provided by Fundação para a Ciência e a Tecnologia of Portugal and IDMEC under LAETA—UID/EMS/50022/2013 and PDTC/EMS-TEC/0626/2014.

1.1 Introduction

The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been developed to optimize solutions and reduce the overall computational costs of large finite element models.

The simplest approach is to apply faster solution techniques by replacing direct equation solvers by iterative equation solvers. There are various types of iterative solvers but the conjugate gradient (CG) iterative solvers proposed by Lanczos (1952) and Hestenes and Stiefel (1952) are among the simplest and more widely used in finite element computer programs.

Despite the advantages of CG iterative solvers, there are two major concerns (and challenges) related to its utilization in finite element modeling of manufacturing processes. First, precision is lost compared to that of direct solvers, because final accuracy depends on the threshold value utilized for accepting the solution, which inevitably results from a compromise between the desired accuracy and the required CPU time. In case small inaccuracies accumulate during finite element modeling of a manufacturing process involving a large number of solution steps, they may lead to poor satisfaction of the boundary conditions and to inaccuracies in fulfilling symmetry conditions. For instance, a zero displacement associated with a symmetry line (or plane) may be computed as a very small nonzero displacement creating problems in the overall final accuracy of the numerical simulation. In problems involving contact the earlier mentioned problems may, for larger threshold values, also disturb the contact algorithms, eventually leading to penetration in contact pairs.

The second drawback results from the fact that CG iterative solvers suffer from low robustness and applicability in case of ill-conditioned equation systems. In fact, iterative solvers have been reported unstable when dealing with ill-conditioned equation systems, whereas direct solvers have proved to be more robust (Farhat and Wilson, 1988). This is particularly relevant for finite element formulations that make use of penalties (i.e., very large numbers) to impose material incompressibility and/or to handle contact between different objects (e.g., deformable vs. deformable objects and/or deformable vs. rigid objects) and for simulations with large rigid body motion (e.g., when a preform is settling into a metal forming die undergoing very little deformation).

Among various improvements to optimize convergence and to improve the CPU time of CG iterative solvers, preconditioning and parallelization have been the most widely used techniques (Meijerink and van der Vorst, 1977).

A more complex approach to optimize solutions and reduce the overall computational cost of large finite element models has ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• List of contributors
• About the editor
• Preface
• 1: Parallel direct solver for finite element modeling of manufacturing processes
• 2: Optimal inspection/actuator placement for robust dimensional compensation in multistage manufacturing processes
• 3: Numerical optimization strategies for springback compensation in sheet metal forming
• 4: Finite element modeling of hot rolling: Steady- and unsteady-state analyses
• 5: Numerical modeling methodologies for friction stir welding process
• 6: Modeling of hard machining
• 7: Multiresponse optimization in wire electric discharge machining (WEDM) of HCHCr steel by integrating response surface methodology (RSM) with differential evolution (DE)
• Index