Behavioral Optimization of Pseudo-Neutral Hole in Hyperelastic Membranes Using Functionally graded Cables

Structures consisting of cables and membranes have been of interest to engineers due to their higher ratio of strength to weight and lower cost compared to other structures. One of the challenges in such structures is presence of holes in membranes, which leads to non-uniform stress and strain distributions, even under uniform far-field deformations. One of the approaches suggested for controlling this non-uniformity is reinforcing the hole edge using a cable, such that stretch changes near the hole are minimized compared to that of the far field in the membrane. In this study, considering an optimization problem, it is illustrated that for different geometries and stretch ratios in a biaxial loading of the membrane, a suitable cable of varying stiffness can be chosen such that stretch non-uniformity in the membrane is minimum, thus presenting a state of a pseudo-neutral hole in the membrane. The presented form of parametric functionally graded cable and the optimization problem solved for a couple of hole shapes show that the cable can induce a state of close to uniform stretch distribution for certain values of far field stretch ratios, it also proves effective for a range of such a ratio. Relative non-uniformity indices as low as 2 percent are achieved from optimization.