Keywords: welding, three-dimensional finite element analysis, explicit time integration, implicit time integration, Abaqus.

In this paper the use of mixed time integration is investigated to increase the efficiency of welding simulation. By finding the right balance in combining the advantages of explicit and implicit time integration methods we hope to come closer to using virtual fabrication to "manufacture" numerical models to be used in virtual experiments both in research and design. This paper focuses on the applicability of explicit time integration in the simulation of welding comparing it to the more commonly used implicit method.

In the simulation of sheet metal forming it is common practice to use the combination of explicit and implicit time integration since it consists of two very different phases each of which suits one of the two solution methods: stamping and springback [1]. The simulation of welding can also be divided into two very distinguishable parts of similar characteristics to those of sheet metal forming: the welding itself and the cooling down that follows.

Based on an example from the initial phase of the research [2] the characteristics of welding simulation are reviewed from the point of view of time discretization. The explicit and implicit time integration methods are compared and the stability requirement of the explicit method is looked at in detail. In order to improve the applicability of explicit method for welding simulation the so called "mass scaling" technique is investigated. Two examples are presented. The first one is a three-dimensional solid finite element recreation of the classic rod model commonly used to demonstrate the development of residual stresses in welded plates. The second example is a butt welded plate also using three-dimensional solid finite elements.

Using ABAQUS/Standard and ABAQUS/Explicit [3] several analyses of these two examples are performed and compared for the cases of implicit analysis, explicit analysis without mass scaling and with different levels of mass scaling. It is demonstrated that by using mass scaling the calculation time of the explicit method can be very significantly reduced to a similar range to that of the implicit analysis. Comparing the results of the analyses it is found that the calculated residual stresses are identical in the implicit analysis and all the explicit analyses. However, distortions seem to be underestimated by the explicit method and when a higher factor of mass scaling is used the difference between the explicit and implicit analyses is greater.

Although the examples of this paper are of small scale, they demonstrate the potential of using mixed time integration for welding analysis simulations. We believe that upon completion of the future tasks identified in this paper an efficient modelling and analysis strategy can be developed to allow analysts of welded steel structures to include realistic imperfections in their numerical models used in performance based design.

1

N. Narasimhan, M. Lovell, "Predicting springback in sheet metal forming: an explicit to implicit sequential solution procedure", Finite Elements in Analysis and Design, 33(1), 29-42, 1999. doi:10.1016/S0168-874X(99)00009-8

2

J. Nézo, B.H.V. Topping, L. Dunai, "Virtual Fabrication of Steel Welded Plate Girders", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 101, 2002. doi:10.4203/ccp.75.101

3

Abaqus Analysis User's Manual, Version 6.7, 2007. www.simulia.com

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