A 1D nonlinear TWB model derived from an assembly of Koiter Shells

In this work, TWBs with open cross sections are considered. At first they are viewed as an assembly of plates each one of them being a wall of the TWB. Each plate is then modeled as a Koiter shell, initially flat. This allows for using the two fundamental forms of the middle surface of the shell as strain measures. On the middle surface of each plate two local coordinates are introduced: we will call them longitudinal and transversal, respectively. It is assumed that the components of the displacement field which characterize the middle surface kinematics can be expressed as a product of two functions: one defined along the longitudinal coordinate and one defined along the transversal coordinate. Given an explicit expression of the latter functions the 2D plate fields are reduced to 1D ones. The functions of the transversal coordinate are chosen so that the stretch along it together with the membrane shear, vanish. It is worth noting that the linearization of these constraints leads to the well known Vlasov’s assumptions. The walls are assembled by imposing suitable boundary conditions on their longitudinal edges. This procedure gives rise to an hyperelastic 1D beam model in which at least the warping is taken into account. The main features of the model are shown by means of some simple applications