Elastic modeling of biopolymer spherical shells

  • Author / Creator
    Zhang, Lei
  • Elastic modeling is essential for mechanical behavior of biopolymer spherical shells [such as ultrasound contrast agents (UCAs), spherical viruses and enzymes] characterized by high structural heterogeneity and geometric imperfection. The effects of structural heterogeneity and geometric imperfection on pressured buckling and free vibration of biopolymer spherical shells are studied in detail in three chapters of this thesis. 1) An axisymmetric geometric imperfection sensitivity analysis is conducted based on a refined shell model recently developed for pressured buckling of biopolymer spherical shells of high structural heterogeneity and thickness nonuniformity. The influence of related parameters (including the ratio of radius to average shell thickness, the ratio of transverse shear modulus to in-plane shear modulus, and the ratio of effective bending thickness to average shell thickness) on imperfection sensitivity is examined for pressured buckling. The actual maximum sustainable external pressures for typical imperfect spherical biopolymer shells (viral capsids and ultrasound contrast agents) are predicted based on physically realistic parameters. 2) Initial post-buckling and geometric imperfection sensitivity of a pressured biopolymer spherical shell based on non-axisymmetric buckling modes and associated mode interaction are studied. The comparison with the results obtained based on the axisymmetric imperfection sensitivity analysis identified the cases in which a more accurate non-axisymmetric analysis with the mode interaction is required for imperfection sensitivity of pressured buckling of biopolymer spherical shells. The implications of the non-axisymmetric analysis to two specific types of biopolymer spherical shells (viral capsids and ultrasound contrast agents) are discussed. 3) A refined shell model is employed to study the effect of high structural heterogeneity on natural frequencies and vibration modes of biopolymer spherical shells. With this model, the structural heterogeneity of a biopolymer spherical shell is characterized by an effective bending thickness and the transverse shear modulus. With physically realistic parameters for spherical viruses and enzymes, the natural frequencies and vibration modes predicted by the present refined shell model are in better agreement with some known simulation results, which suggest that the refined shell model could offer a relatively simple model to simulate free vibration of biopolymer spherical shells of high structural heterogeneity. The theoretical models and numerical results achieved in this thesis help clarify to what degree the structural heterogeneity and geometric imperfection in biopolymer spherical shells affect their global mechanical response such as pressured buckling and free vibration. Using physically realistic parameters for some typical biopolymer spherical shells, the predictions of actual maximum sustainable pressure and natural frequencies and associated vibration modes provide plausible comparisons with known simulations and experiments of specific biopolymer spherical shells.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.