Large bending behavior of creased paperboard. II. Structural analysis

The mechanics of a paradigmatic typical carton corner with five creases is analyzed theoretically, in closed form. A general kinematical analysis of the mechanism (in finite rotation) is presented, assuming the versor of the intermediate crease, s, as a 2-degree-of-freedom Lagrangian parameter. The rotation hc of the cth crease is derived, together with the existence domain and a discussion of the singular configurations. The actions, driving the carton during a prescribed quasi-static erection program, are derived in a very efficient manner using the Virtual Works Equation, taking into account a non-linear anholonomic bending constitutive law of the creased paperboard. In particular, the active and reactive components of the moment /, driving s along its path, are identified. No resort to the tangent stiffness computation is required. Some numerical examples illustrate the rotation and the driving forces obtained for both monotone- loading and complex loading–unloading erection paths. The presented results, ‘‘exact’’ within the scope of the restrictive hypotheses assumed, may be used in a preliminary design approach as well as a benchmark for more realistic FEM or CAE simulators