The effect of local random defects on the response of pantographic sheets

In the last decade, pantographic structures have attracted the attention of many scientists because of their exotic mechanical behaviors. Despite several studies conducted on this field, probabilistic remarks cannot be found in the literature. This paper aims to fill this gap by providing the first stochastic study on pantographic sheets. A new simplified procedure is proposed to investigate the effects of local axial, bending, and torsional defects on their mechanical responses. The suggested approach involves a generalization of an existing theoretical result and the use of Monte Carlo simulations to derive probability density functions, mean values, standard deviations, and coefficients of variation of the random kinematic unknowns. It, surely, can be applied to any mechanical system. The achieved results allow stating that pantographic structures are not particularly affected by local random defects thanks to their redundant and complex microstructures. Moreover, the interdependencies among their substructures, beams, and pivots, make it not easy to find the positions of defects that minimize, once fixed all the other things, the randomness of the mechanical responses. A minimization problem should be solved and a work on this topic is in progress.