Parallel Processing Of Forging Simulation ByUpper Bound Elemental Technique

Abstract

Presented in this paper are parallel algorithms developed for simulation of forging and extrusion type operations on a Distributed Array Processor (DAP) by Upper Bound Elemental Technique (UBET). Particular attention is paid to the parallel solution of UBET by optimization techniques. The UBET approach, its formulation, and suitable parallel algorithms are presented, and discussions are made on the parallel algorithms for the UBET calculation and optimization processes. Results of the parallel algorithms on the DAP are evaluated in comparison with that of a serial approach on a mainframe computer. INTRODUCTION The Upper Bound Elemental Technique (UBET) is one of the major numerical techniques that have been developed for computerised simulation of forging and exTransactions on Information and Communications Technologies vol 3, © 1993 WIT Press, www.witpress.com, ISSN 1743-3517 96 Applications of Supercomputers in Engineering trusion type operations. Initially, this technique was developed for predicting loads in complex forging processes by McDermott and Bramley [1] in 1974, based on the upper bound theory and the UBA (Upper Bound Approach) due to Kudo [2]. Some 5 years later, Osman and Bramley [3] further developed the UBET to predict both loads and metal flow in forging and extrusion type operations through process simulation in an incremental manner. Later development has expanded the power of UBET to accommodate other predictions. These include the prediction of pressure distribution along the die-workpiece interfaces [4], and the prediction of preform shape of the workpiece. The latter was achieved by simulating a forging process in a reverse manner from the desired final shape [5]. The basic approach of the UBET is to divide the entire movement of the die into a number of increments. At each increment, the workpiece is divided into a number of generalised elements. A predefined mathematical model is imposed on each of the elements based on approximations to energy dissipation by upper bound theorem. The solution for the total energy dissipation of all the elements, which is the load required to perform the desired forging, is aimed at obtaining a kinematically acceptable velocity field which minimizes the load requirement. From the upper bound point of view, a load so obtained is most close to reality. The optimization process for the UBET solution is performed by taking the UBET calculation as the objective function and the velocity components as variables. Before a satisfactory solution is reached, thousands of times of function calculation are usually needed. Moreover, the optimization process has to be performed at each increment during the entire simulation, resulting in a high demand on computational time especially when a large number of elements are involved. In order to reduce the computational time, the use of a faster computer is always a choice. However, the performance of a serial computer has a limit and the use of a supercomputer can be costly and not easily accessible. For the foreseeable future, the massively parallel computers, such as the Distributed Array Processor (DAP) [6,7], should be able to offer a better solution. This type of computers uses relatively much cheaper technology in individual processors while offering a huge number of processors capable of performing an instruction on a massive number of data concurrently. This makes it cost-effective. The problem is that the development of relevant parallel algorithms requires a different way of thinking and implementation from that of serial algorithms, and often demands some modifications on the existing mathematical models. However, efforts of developing the parallel algorithms can be offset by the gain in computational speed and efficiency, saving time and cost on operation. This paper is devoted to the development of parallel algorithms for the UBET calculation and its solution by optimization techniques on a massively parallel computer. For this purpose, a brief introduction to UBET is given, the UBET formulae and their implementation on massively parallel computers is presented, and different parallel approaches are discussed. Finally, results obtained on an example problem using both parallel and serial approaches are analysed. Transactions on Information and Communications Technologies vol 3, © 1993 WIT Press, www.witpress.com, ISSN 1743-3517 Applications of Supercomputers in Engineering 97 THE UPPER BOUND ELEMENTAL TECHNIQUE The upper bound approach to the prediction of forging loads considers only the conditions which must be fulfilled by the strain increments in a fully plastic body, ignoring the stress equilibrium [8,9]. The theory of this approach is based on one of the limit analysis theorems where the rate of work estimated for material undergoing plastic deformation is certain to be greater than or equal to the actual one. The actual expression for an estimate of the working load in the upper bound approach can be referred to the work due to Drucher et al [10] which may be written as