西安交通大学114周年校庆暨航天航空学院成立5周年系列学术报告一
讲座名称：
西安交通大学114周年校庆暨航天航空学院成立5周年系列学术报告一
讲座时间：
2010-04-07
讲座人：
罗小玉
形式：
校区：
兴庆校区
实践学分：
讲座内容：
Buckling and finite deformation of
a hyper-elastic tube under external pressure
X. Y. Luo
Department of Mathematics
University of Glasgow
UK
Cylindrical tube deforms in a strongly nonlinear fashion when subject to large external pressure, a problem that frequently appears in many biological applications. Engineering approaches to this problem often used linear deformation, which can give very inaccurate predictions. In this work, a geometric and material nonlinear analysis is conducted for axisymmetric deformation of a thick-walled cylindrical tube subject to external pressure, and the results are compared to the linear predictions. The formulation is fully nonlinear and the governing system of nonlinear partial differential equations is derived and solved numerically using the C++ based object-oriented finite element library Libmesh. The weighted residual-Galerkin method and the Newton-Krylov nonlinear solver are adopted for solving the governing equations. Since the nonlinear problem is highly sensitive to small changes in the numerical scheme, convergence was obtained only when the analytical Jacobian matrix was used. It is found that for small deformation, both linear and nonlinear models give very similar results. However, cylindrical tubes behaves very differently under large external pressure, and the dominate features are the corner bulging and higher modes. This is the first time that a totally nonlinear analysis is carried out for thick walled tubes, and the results may have significant implications to many physiological applications involving soft vessels undergoing large deformation.
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