The scaled boundary FEM for nonlinear problems

✍ Scribed by Zhiliang Lin; Shijun Liao

• Book ID: 104012719
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 827 KB
• Volume: 16
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2010.03.005

✦ Synopsis

The traditional scaled boundary finite-element method (SBFEM) is a rather efficient semianalytical technique widely applied in engineering, which is however valid mostly for linear differential equations. In this paper, the traditional SBFEM is combined with the homotopy analysis method (HAM), an analytic technique for strongly nonlinear problems: a nonlinear equation is first transformed into a series of linear equations by means of the HAM, and then solved by the traditional SBFEM. In this way, the traditional SBFEM is extended to nonlinear differential equations. A nonlinear heat transfer problem is used as an example to show the validity and computational efficiency of this new SBFEM.