Quadrilateral Isoparametric Shear Deformable Shell Element for Use in Soil-Structure Interaction Problems

Abstract

In the finite-element analysis of soil-structure interaction problems, shell elements are important to model structural components such as tunnel linings or sheet pile walls. In this paper the development, implementation, and testing of a curved quadrilateral isoparametric shear deformable shell element are presented. An overriding concern in the analysis of soil-structure interaction problems is the $C^0$ compatibility of the shell elements with the solid elements used to model the soil. Many recent publications on shell elements deal with the elements in a purely structural context and therefore do not require the $C^0$ compatibility with solid elements. The development of the shell element presented here forms an extension of a new approach to curved Mindlin and axisymmetric shell elements introduced by Day and Potts in 1990. There are no generally accepted benchmarking marking problems for the use of shell elements in three-dimensional geotechnical engineering problems. Consequently, the performance of the shell element is first assessed by analyzing standard structural benchmarking problems. It is found that the new element performs well compared to other elements used in a purely structural context. Further, it is demonstrated that the same element that is used to analyze curved shells can be used to analyze flat plates without the requirement of a different formulation. Finally, the performance of the new shell element is compared with a closed form solution in the analysis of a deep tunnel.