In this paper we present a 2D four-parameter model that accounts for the variation of transverse deformation through-the-thickness in thick linear elastic shells. This model is deduced directly from the 3D elasticity equations of the traction-displacement boundary value problem. Transverse shear strains and thickness variation are accountable through additional terms which appear in the final equations besides well-known terms in the classical Kirchhoff-Love models for thin shells. A unique solution of the variational equation is established, and numerical and analytical results are compared with satisfaction.

The article focuses on the influence of differential shrinkage linked by drying at the early-age displacements and strain distribution of a concrete ring specimen. Depending on the gradient of dimension changes through the thickness, tensile stress occurs near the exposed surface where drying is greater and thus results in strain gradients development. An experimental design was carried out on a concrete ring cast in laboratory conditions in order to monitor strains and displacements. Subsequently, a finite element method was used to simulate the ring’s behaviour in drying conditions. The gradient development linked by a non-uniform moisture distribution in the thickness is established by solving the non-linear partial differential drying equation with Mensi’s diffusion law. The stress and displacement analysis was modeled by three nodes curved shell FEM (CSFE-sh) based on strain approximation with the shell theory. Finally, the ring’s behaviour includes both differential shrinkage resulting in the mechanical and physical properties of gradients development in the thickness and the influence of prestressing, in which the tensile creep effects have a great influence. The comparison of experimental results with numerical simulation shows that drying and tensile creep phenomena have the most important influence on the early-age stress development in the walled ring.

Concrete shells are widespread in civil engineering constructions. Because of the moldability of concrete, special structures such as domes, bridge caissons, buried or raised reservoirs, and arch dams are built with concrete. In this study, we are particularly interested in the variation of the thickness and the resulting strains during a short-term mechanical loading of a concrete ring in its elastic phase. On the one hand, transverse stresses through the thickness are calculated numerically by implementing a particular family of finite elements (four degrees of freedom per summit node) with a two-dimensional shell model, which accounts for thickness variations and transverse distortions. On the other hand, an experimental device was mounted in order to validate numerical predictions.