Date of Award

December 2020

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Teng Zhang

Second Advisor

Zhao Qin


annular thin sheet, cylindrical thin shell, discrete shell model, energy landscape, wrinkle pattern

Subject Categories



The study of morphological instabilities in thin solids, such as buckling of thin shells and wrinkling of thin sheets, is of growing interest to a number of academic disciplines including en-gineering, physics, biology, and many others. For example, buckling has traditionally been re-garded as an unfavorable phenomenon in engineering design, but emerging technologies con-sider such behavior as an opportunity for novel functionality. The formation of wrinkle patterns on thin sheets has also emerged rapidly as canonical problems to investigate pattern formation in the physics community. The nonlinearities of the post-buckling behaviors encountered in these problems make theoretical analysis a challenging endeavor, thus highlighting the important role of numerical methods in the study of these problems. Our modeling and simulations of several prototypical instability problems – the buckling of spherical cap shells and cylindrical shells, and the wrinkling of annular sheets – reveal the complex post-buckling morphologies and energy landscapes. Our computational frameworks are promising for a wide range of applications, such as designing robust thin shell structures, developing buckling-induced smart devices, and ex-plaining pattern formation in disordered systems.


Open Access

Included in

Engineering Commons