Modal Analysis of Three-Dimensional Finite Element Models of Reinforced Concrete Structures

ABSTRACT

In this article modal analysis of reinforced concrete structures by the Finite Element Method is reviewed. A list of simplifications – implemented within idealization of the structural scheme at the calculation phase – that reduce the reliability of the results is provided. Out of the necessity to use idealizations, the Finite Element Method allows for the possibility of creating multiple alternative computational models for each structural model respectively, and there are many alternative calculation results. Consequently, the calculation of reinforced concrete structures always leads to more than a single result. Idealization of geometric shape has the greatest influence on the variability of results. Accordingly, the need to use solid finite elements in calculations of reinforced concrete structures including rod and slab elements becomes apparent. This will provide means to abandon the subjective construction of the design model of the structure. In addition to traditional calculations of the stress-strain state from the action of static load for a number of structures, a modal analysis should be performed (dynamic calculation). Its purpose is to determine the shapes and free oscillation frequencies in order to determine the correctness of the structural scheme by the first shapes and compare the values of natural frequencies with the regulatory requirements. Since the significant need for computational resources poses a natural limitation of the use of solid finite element models for modal analysis, the effectiveness of this method of calculation should be established. The article showed the effect of applying the idealization of the geometric shape on the results of the modal analysis by comparing two calculations of the FEM of one structure and concluded that solid finite elements should be used for the calculation of reinforced concrete frame structures.

1. Pacoste C., Plos M., Johansson M. Recommendations for finite element analysis for the design of reinforced concrete slabs. KTH, Stockholm, Sweden 2012. 55 p.
2. Düster A., Rank E., Szabó B. The p-Version of the Finite Element and Finite Cell Methods. September 2017. In book: Encyclopedia of Computational Mechanics. 2nd Edition. Publisher: John Wiley & Sons, Ltd., Editors: Erwin Stein, René de Borst, Thomas J.R. Hughes.
3. Smirnov A. F., Aleksandrov A. V., Lashchenikov B. Ja., Shaposhnikov N. N. Stroitelnaya mehanika. Dinamika i ustoichivost sooruzheniy [Structural theory. Dynamics and stability of structures]. Moscow : Stroyizdat, 1984. 414 p. (rus)