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Simplified finite element analysis missile impact on reinforced concrete structures with attached equipment

Abstract of the technical paper/presentation presented at:
19th International Symposium on Interaction of the Effects of Munitions with Structures (ISIEMS 19), September 19–23, 2022, Dresden, Germany

Prepared by:
Genadijs Sagals and Thambiayah Nitheanandan
Canadian Nuclear Safety Commission


This paper describes the work conducted by the Canadian Nuclear Safety Commission (CNSC) to improve understanding of reinforced concrete (RC) structure under missile impact using numerical simulations and comparing them against tests. Finite Element Analysis of the missile impact was conducted. Subsequent propagation of impact -induced vibrations through the RC structure and post-impact vibrations of attached simplified equipment were also examined. Several assumptions and simplifications were introduced to significantly reduce modeling time for large structures as described below. Finite Element predictions were compared with test results.

The concrete mock-up with two simple structures attached, one welded and another bolted, was built and tested at the VTT Technical Research Centre in Espoo, Finland. This mock-up was impacted by three consecutive missiles with varying velocities in order to obtain the damage accumulation. To examine vibration transmission through the mock-up, two simple structures imitating welded and bolted equipment were attached to the rear wall of the structure, while the missile impact was at the centre of the front wall. The parameters of the missiles and the RC structure were selected to ensure flexible behaviour of the RC target in the impact area with only moderate damages, specifically cracking and permanent deformation without perforation.

The non-linear dynamic behaviour of the reinforced concrete slabs under missile impact was analyzed using the commercial finite element (FE) code LS-DYNA. A hybrid FE model using both 3-D solid and 2-D shell FE models was developed for the target discretization. Since the ultimate objective of this work is to model the entire structure over long time periods, a simplified combined shell-solid model with distributed (smeared) reinforcement was selected and validated. This model employs solid FE around an impact area and shell FE for the rest of the mock-up.

Detailed modelling of a large RC structure with all equipment attached leads to a very large FE model. Therefore, two-level FE modelling using a sub-modelling approach was employed: first, the vibrations of a reinforced concrete structure with a simplified equipment model were analyzed, and second, detailed analysis of attached equipment was conducted. This approach assumes uncoupled dynamic behaviour of the structure and the equipment. While the sub-modelling technique is commonly used in static analysis, a special sensitivity analysis was conducted to prove the applicability of sub-modelling for impact analysis.

Finally, the effect of structural damping was examined, and the best possible damping was selected. The selected damping values and sub-models resulted in relatively good agreement with the test results for both global (RC mock-up) and local (equipment) behaviour.

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