Buckling of ellipsoid grid-shells made of smooth triaxial weaving with naturally in-plane curved ribbons

Triaxial weaving can form two-dimensional structures into three-dimensional structures using initially straight and flat ribbons. However, most of the 3D structures fabricated with conventional weaving methods using straight ribbons have some topological defects. To obtain smoother 3D surface structures, Baek proposed a novel weaving method using naturally curved (in-plane) ribbons to fabricate three-dimensional curved structures. We believe that an ellipsoidal weave with smooth geometric properties must have new mechanical properties. To this end, the buckling behavior of an ellipsoidal weave with naturally in-plane curved ribbons is investigated with a test and dimensional analysis in this research. The results of the calculations and experiments show that the failure modes of an ellipsoidal weave under vertical loading are divided into the inward deformation of the ribbon, overall wave buckling, and "blister"buckling along the strong radius. The aspect ratios, ribbon width, and thickness have a great effect on the buckling behavior of ellipsoidal weaves. The high load capacity and strong stability of ellipsoidal weaves with thicker or wider ribbons are exhibited. Moreover, the geometric size limit of the curved ribbons of an ellipsoidal weave is obtained with experiments. In addition, in this research, the buckling load equation and initial stiffness equation for an ellipsoidal weave are proposed using the method of testing and theoretical analysis. Our study can provide a theoretical basis for the stable design of an ellipsoidal weave structure.