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Computational Inverse Analysis of Pre-stressed Concrete Structures

Figure: Vasco da Gama Bridge (PBWORKS, 2011)

Project Leader: Dr Sebastian Skatulla

Since its inception, pre-stressed concrete has evolved and established itself as an important structural material. From bridges to nuclear power vessels, from building serving every use to monumental towers, pre-stressed concrete has various structural applications nowadays. New and innovative pre-stressed concrete design relies on adequate means of analysis, in particular computational modelling. The conventional computational approach in the analysis of pre-stressed concrete consists of using a forward analysis method, whereby the final stress of the deformed concrete can be calculated after being subjected to different loading conditions. The forward analysis is well-accepted in structural design, as it considers, besides structural layout, dimensions, concrete material properties and reinforcement, all applicable loading conditions in their chronological order. However, limits imposed on stress and deformation of the structure under loads render structural analysis and design to an iterative process. The required time for this process can be significantly reduced by making use of a so-called inverse design analysis or “backward analysis”.

Figure: Inverse analysis step

1: Determine unknown unloaded state from a known deformed state due the known service loads.

Figure: Inverse analysis step 2: Determine the necessary pre-stressing which is in balance with the service loads such that the member is straight.

It facilitates the computation of the stress-free configuration of the pre-stressed structure taking the deformed state of structure under loading as a starting point and working backward to the initial undeformed reference state. These kinds approaches have been already successfully utilized, e.g. for incompressible rubber material (Govindjee and Mihalic 1996) and biological soft tissue (Rajagopal et al. 2007, Gee et al. 2010).

This work aims at the development and validation of an inverse computation method in the analysis of pre-stressed concrete members. The method is based on a total Lagrangian approach considering finite strains and non-linear hypoelastic material. It is implemented in the in-house structural analysis software SESKA to perform the computations.

References
Gee, M. W., Förster, C., & Wall, W. A. (2010). “A computational strategy for prestressing patient‐specific biomechanical problems under finite deformation”. International Journal for Numerical Methods in Biomedical Engineering, 26(1), 52-72.

Govindjee, S., and Mihalic, P.A. (1996). "Computational methods for inverse finite elastostatics." Computer Methods in Applied Mechanics and Engineering 136(1): 47-57.

Rajagopal, V., Chung, J., Bullivant, D., Nielsen, P.M. & Nash, M.P. (2007). Determining the finite elasticity reference state from a loaded configuration. International Journal for Numerical Methods in Engineering. 72(12):1434-1451.