Author: Wong, Shun-man Title: The bifurcation analysis of thick-walled hollow cylinders by a semi-analytical approach under different internal and external pressures Degree: M.Sc. Year: 2002 Subject: Hong Kong Polytechnic University -- DissertationsCylindersStrains and stressesBifurcation theory Department: Multi-disciplinary StudiesDepartment of Civil and Structural Engineering Pages: vi, 252 p. : ill. (chiefly col.) ; 30 cm Language: English Abstract: A semi-analytic approach is proposed by Chau (1998) in obtaining the eigenstress at the onset of geometric (or diffuse mode) bifurcations in thick-walled hollow cylinders under different external and internal pressures. This approach utilizes the solution obtained recently by Chau and Choi (1998) as a fundamental solution, in which the eigenstress for bifurcation is derived analytically for equal internal and external pressures. The thick-walled cylinders can be divided into a number of "ring elements", each of them can be modelled approximately by fundamental solutions obtained by Chau and Choi (1998), then compatibility conditions of velocities and traction rates are enforced between the interfaces of the neighbouring ring elements. In this way, the stress variations along the radial co-ordinate can be modelled approximately by allowing a jump in stress field across the interfaces of neighbouring rings since uniform stress field is assumed as the primary solution for each ring. Thus, a traction-velocity (E-F) matrix is formed by compiling the compatibility conditions of velocities and tractions in each interface as well as the boundary conditions at the two free surfaces, both internally and externally. The eigen-values of matrix are the bifurcation stresses at the onset of bifurcation. Since the order of the determinant of the traction-velocity matrix is six times of the number of ring elements, a Program "Bifurcation 2002" is thus developed in this dissertation for calculating the eigenstresses at bifurcation. After compromising the calculation accuracy and computing time, the analyses can then be carried out in ten numbers of rings with good convergence of results. As the material is characterized by Rudnicki's (1977) incremental linear, time- and rate-independent constitutive model, the eigenstresses at the onset bifurcation can be calculated by varying different geometrical parameters of the hollow circular cylinder.

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