The Effect of Mesh Sizing Toward Deformation Result in Computational Dynamic Simulation for Blast Loading Application

The finite element approach was used in the simulation analysis to solve many engineering problems. One of the accuracy factors of this method is dependent on the choice of appropriate element size or mesh discretization. Good mesh discretization can reduce the percentage of error; avoid the computation time approaches to non-practical limits and furthermore, produces the optimal results. The purpose of this study is to identify the best size of mesh elements to be used in the problem analysis using the AUTODYN numerical simulation. The fully clamped circular plate subjected to blast load as per experimental setup was modified and simplified in the two-dimensional (2D) simulation model; it will be seen as a clamped beam at both edges. Plate model were discretized to form nodal and element. The deformation or deflection result found to converge at certain value by increasing the total number of element discretization. Assumed that the deformation results were accurate at the converged state; it will be taken as reference to choose the finest size of mesh element. In this study, several mesh sizes been considered, and the appropriate optimum mesh discretization obtained at range of 0.5 mm to 1 mm.


Introduction
Analysis the behaviour of the structure when subjected to blast loading by using the numerical simulation has been developed with several techniques.Results obtained in the simulation then compared with experimental for validation purpose, thus contributes to reduction of the total experiments need to be carried out.With the rapid development of computing technology in the recent years, researchers have focused on the numerical simulation which is more convenient and economical.
AUTODYN is one hyrocode program used to resolve problems involving the interaction of structural, fluid and gas simultaneously.This application normally used in the blast and ballistic analysis.Integration of pre-processor, post processors and analysis execution code found in this software make it easier to use and more user-friendly.AUTODYN also allows different solver (or processor) as Lagrange, Euler to function simultaneously in a one model analysis.Daniel (2009) used AUTODYN 3D to analyse the effect of blast toward stand-off distance in blast test, and he studied the propagation of wave explosion in the confinement area.Amstrong and Walley (2008) used the Johnson Cook constituting equation in AUTODYN to estimate temperature rises within the crystals in the analysis dynamic recrystallization and spallation or fragmentation.
There are three types of Eulerian solver in AUTODYN: Euler, Euler Godunov and Euler Flux Corrected Transport (FCT Euler).Euler solver used in AUTODYN 2D is based on first-order approach.It allows multi-material to be modelled.However, for second order scheme is only available in AUTODYN 3D.Eulerian element size 5, 2.5, 1.25, 1, 0.625 and 0.5 mm used in order to analyse the effect of mesh sensitivity toward the result.The appropriate meshing size obtained then used for future analysis.

Simulation Model
The modified simulation model carried out referring to experiment has performed by Neuberger, Peles, and Rittel (2009).The experimental setup was shown in Figure 1.The circular target plate with diameter 1000 mm clamped with two thick armor steel ring, tighten together with bolt and clamped, while 8.75 kg of TNT explosive charge with 0.2 m stand-off in distance.In 2D simulation the target seen as a beam and in this experiment TNT were modified using only 1.1 kg in order to avoid element distortion during analysis.The cross sectional diagram and involve parameter shown in Figure 2.  (Neuberger, Peles, & Rittel, 2009) The simulation conducted using high speed computer processor Intel® Core™ i7-2600K CPU@ 3.40 GHz (8CPUs), 3.7 GHz.A 2D axis-symmetric model was developed using Langrage and Multi-Material Euler solver.The model was created in the domain size 500 mm x 450 mm defined as air symmetry in x-axis.Material properties of Steel 1006 with Johnson Cook material model found available in AUTODYN libraries were used to represent the plate.Ideal gas equation of state was chosen to describe air and Jones Wilkins Lee (JWL) equation of state describes the TNT explosive charge.Eulerian elements were used to represent air and TNT and Langrage element were used to represent the plate.Four gauge were pasted at the plate as shown in Figure 3. Gauge 1, 2, 3 and 4 were located at 250 mm, 125 mm, 100 mm and 50 mm respectively from symmetrical axis and plate were fully clamped at the end of the edge.

Conclusions
Model simplification is a very important in simulation analysis.The ability to simplify the model facilitates an analysis by shorten the time taken and produce good results.The selection of mesh size found to be one of the factors to determine the accuracy of the results produced.Common error occurs in simulation analysis is due to the insufficient of refinement finite element grid.
Noted that the number of elements or grid that too much also causes the computation time approaches to non-practical limit and also sometime the results found not promising.In this case, the selection of the mesh found to be in the range from 0.5 mm to 1 mm considered as the best element size for the analysis using AUTODYN software.

Figure
Figure 4. D