Geometric Mechanism of Crease Formation on Twisting Cylindrical Shell

Li-Min Wang^1*, Sung-Ting Tsai², Chih-yu Lee³, Yan-yuChan³, Tzay-Ming Hong¹

¹physics, National Tsing Hua University, Hsinchu,, Taiwan
²Institute for Physical Science and Tech- nology, University of Maryland, College Park 20742, U.S.A, USA
³National 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