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Title: On a nonlinear model for stress-induced phase transitions in a slender compressible hyperelastic cylinder : analytical solutions and stability
Other Titles: Xi chang chao tan xing gan de ying li yin qi de xiang bian : jie xi jie he wen ding xing fen xi
細長超彈性杆的應力引起的相變 : 解析解和穩定性分析
Authors: Ng, Kwok-tim (伍國添)
Department: Department of Mathematics
Degree: Master of Philosophy
Issue Date: 2010
Publisher: City University of Hong Kong
Subjects: Boundary value problems -- Numerical solutions.
Nonlinear theories.
Bifurcation theory.
Notes: CityU Call Number: QA379 .N39 2010
iii, 99 leaves : ill. 30 cm.
Thesis (M.Phil.)--City University of Hong Kong, 2010.
Includes bibliographical references (leaves 78-80)
Type: thesis
Abstract: In this thesis, some methodology in nonlinear dynamics is used to study a boundary-value problem of a nonlinear model arisen in phase transitions in a slender cylinder composed of a compressible hyperelastic material. We transform the original system of boundary value problem to an initial-value (dynamical) problem of finding periodic solutions of coupled nonlinear autonomous oscillators in a four-dimensional space. Hopf-like bifurcation analysis of the periodic solutions of the system is studied. Both analytical and numerical solutions are obtained by using a nonlinear transformation formulation. The analytical solutions are obtained by the perturbation method incorporate with a nonlinear transformation while the numerical solutions are obtained by the perturbation-incremental method. In addition, the accuracy of analytical solutions is investigated by comparing with the numerical solutions. The engineering stress-strain curve is plotted and compared with that from the normal form equation, which is a simplification of the original system. The stability of periodic solutions is also discussed in this thesis.
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