Modelling the third kind boundary condition in scaled boundary finite element method based numerical analysis

Numerical models to deal with the third kind boundary condition (TKBC) are presented under the framework of Scaled Boundary Finite Element Method (SBFEM) for the 2-D static analysis. A gradient based algorithm is presented to tackle with nonlinear TKBC, and a temporally-piecewise adaptive algorithm is developed for a kind of time dependent TKBC. In addition, a proof that the appended stiffness matrix is block-circulant is given if the TKBC is cyclically symmetric, resulting in a reduction of computational expense of SBFEM based numerical analysis. Numerical examples are provided to verify proposed approaches, and satisfactory results are obtained.