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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. • Studied the buckling behavior of ellipsoidal grid-shells by experimental. • The failure mode of ellipsoidal weave with naturally curved ribbons are investigated. • Width and thickness of ribbons on the buckling behavior of the ellipsoidal weaves. • The buckling load equation and initial stiffness of ellipsoidal weaves are carried out. [ABSTRACT FROM AUTHOR]

The Gol'denveizer problem of a torus can be simply described as follows: the inner and outer equator of the torus shell is loaded by the vertical opposite balanced forces. Gol'denveizer proposed that the membrane theory of shells does not yield a valid solution to this problem. Following this, Audoly and Pomeau used a membrane theory of a toroidal shell and nonlinear boundary-layer to study the linear Gol'denveizer problem and gave a simple solution relating resultant force F and vertical displacement. Sun used the bending theory of shells to solve the linear Gol'denveizer problem, and demonstrated that the solution by Audoly and Pomeau for the linear Gol'denveizer problem is extremely accurate. However, to the best of our knowledge, no one has examined the nonlinear Gol'denveizer problem. In this study, the finite element method is used to observe the nonlinear mechanical property and buckling of the Gol'denveizer problem of a circular and elliptic torus. Investigations reveal that the radius ratios a / R and a / b have great influences on the deformation and force of a circular torus and elliptical torus, respectively, and that the negative Gaussian part of a torus has a stronger bearing than the positive Gaussian part. Additionally, when the vertical force is large enough, shear buckling may occur in the circular and elliptic tori. We propose the buckling failure modes of circular and elliptical torus. As a / b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually. • Studied the nonlinear Gol'denveizer problem of torus shells by using FEM. • Identified the negative Gaussian part of circular torus has a stronger bearing. • Force and displacement of circular tori are not equal to zero at crown line. • Studied the buckling behaviors of Gol'denveizer's problem of half-circular tori. • Found a new buckling phenomenon that called a "skirt" shape. [ABSTRACT FROM AUTHOR]