Geometric Mechanism of Crease Formation on Twisting Cylindrical Shell Li-Min Wang ^{1*}, Sung-Ting Tsai^{2}, Chih-yu Lee^{3}, Yan-yuChan^{3}, Tzay-Ming Hong^{1}^{1}physics, National Tsing Hua University, Hsinchu,, Taiwan^{2}Institute for Physical Science and Tech- nology, University of Maryland, College Park 20742, U.S.A, USA^{3}National Hsinchu Senior High School, Hsinchu,, Taiwan* Presenter:Li-Min Wang, email:wang850308@gmail.com This thesis discuss the mechanism of regular creases’ pattern formation due
to twisting buckling under different geometry constraints. Discovering the number of creases N can unique determined by the ratio of radius R and width w of cylindrical shell, a 2D parameter, N = N(R/w). We get analytic solutions that fits the experimental data from simple geometry, energy minimization and two new material properties. These new properties display more concise than ordinary material properties used in elastic-plastic mechanics. In addition to N, R/w can be used to depict three types of creases: fracture, regular and irregular. This thesis also allow us to build a bridge between small and large deformation problem form simple and analytic results instead of numerical solutions of von Kármán–Donnell equations which are complicated. Beside the simplest case, cylindrical shell, we extend this problem to truncated cone, polygon cylindrical shell, beveled end pipe and ball, trying to unify the influence of material and geometry. According to the scaling property of types of creases, we apply the result to explain of creases of earth’s plates, the formation of mountains, and propose the twisting buckling mechanism of deformation of earth’s plates. Keywords: large deformation problem, buckling, Crease formation, Geometric, twisting |