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Nonlinear analysis of RC shell structures using multilevel modelling techniques

Smitha Gopinath (Structural Engineering Research Centre, CSIR, Chennai, India)
Nagesh Iyer (Structural Engineering Research Centre, CSIR, Chennai, India)
J. Rajasankar (Shock and Vibration Group, Structural Engineering Research Centre, CSIR, Chennai, India)
Sandra D'Souza (Computational Structural Mechanics Group, Structural Engineering Research Centre, CSIR, Pune, India)

Engineering Computations

ISSN: 0264-4401

Article publication date: 24 February 2012



The purpose of this paper is to present integrated methodologies based on multilevel modelling concepts for finite element analysis (FEA) of reinforced concrete (RC) shell structures, with specific reference to account for the nonlinear behaviour of cracked concrete and the other associated features.


Geometric representation of the shell is enabled through multiple concrete layers. Composite characteristic of concrete is accounted by assigning different material properties to the layers. Steel reinforcement is smeared into selected concrete layers according to its position in the RC shell. The integrated model concurrently accounts for nonlinear effects due to tensile cracking, bond slip and nonlinear stress‐strain relation of concrete in compression. Smeared crack model having crack rotation capability is used to include the influence of tensile cracking of concrete. Propagation and change in direction of crack along thickness of shell with increase in load and deformation are traced using the layered geometry model. Relative movement between reinforcing steel and adjacent concrete is modelled using a compatible bond‐slip model validated earlier by the authors. Nonlinear iterative solution technique with imposed displacement in incremental form is adopted so that structures with local instabilities or strain softening can also be analysed.


Proposed methodologies are validated by evaluating ultimate strength of two RC shell structures. Nonlinear response of McNeice slab is found to compare well with that of experiment available in literature. Then, a RC cooling tower is analysed for factored wind loads to study its behaviour near ultimate load. Numerical validation demonstrates efficacy and usefullness of the proposed methodologies for nonlinear FEA of RC shell structures.


The present paper integrates critical methodologies used for behaviour modelling of concrete and reinforcement with the physical interaction among them. The study is unique by considering interaction of tensile cracking and bond‐slip which are the main contributors to nonlinearity in the nonlinear response of RC shell structures. Further, industrial application of the proposed modelling strategy is demonstrated by analysing a RC cooling tower shell for its nonlinear response. It is observed that the proposed methodologies in the integrated manner are unique and provide stability in nonlinear analysis of RC shell structures.



Gopinath, S., Iyer, N., Rajasankar, J. and D'Souza, S. (2012), "Nonlinear analysis of RC shell structures using multilevel modelling techniques", Engineering Computations, Vol. 29 No. 2, pp. 104-124.



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