hp-adaptive finite element analysis of thin-walled structures with use of the shell-to-shell transition elements

In this paper we consider hp-adaptive finite element analysis of thin-walled structures (plates and shells) with use of the adaptive shell-to-shell transition elements. Such elements are necessary in the case of complex mechanical description, i.e. when first-order shell and higher-order shell models are employed together for the mechanical characteristics of a thin-walled member. In such a case the transition model is necessary in order to change the plane stress and the lack of elongation of the lines perpendicular do the mid-surface, both valid in the first-order model, into the three-dimensional stress and strain states of the higher-order shell models. Our transition models are discretized with combined hp/hpq-approximations, where the longitudinal and transverse orders p and q, respectively, and the averaged dimension h of the transition element can vary adaptively. Note that in the case of the pure models, i.e. the first-order and higher-order shell models, we employ two-dimensional, hp, and hierarchical, three-dimensional, hpq, adaptive approximations, respectively. Our hitherto works concerned parametric (non-adaptive) studies of various transition models in the contexts of: hierarchical modelling effectivity, hierarchical approximations effectivity, and error estimation effectivity as well. In this paper we present the effectivity analysis of hp-adaptive procedures in the case of the transition models employed. This effectivity is compared to the cases of the pure, either first-order or higher-order, shell models of thin-walled structures.