Open AccessA new meshless method using Taylor series to solve elasticity problems
Author(s) -
Yendoubouam Tampango,
Michel PotierFerry,
Yao Koutsawa,
Salim Belouettar
Publication year - 2012
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/17797179.2012.721500
Subject(s) - taylor series , radius of convergence , mathematics , regularized meshless method , exponential function , mathematical analysis , elasticity (physics) , robustness (evolution) , convergence (economics) , boundary value problem , series (stratigraphy) , singular boundary method , power series , finite element method , boundary element method , biochemistry , chemistry , physics , materials science , gene , economics , composite material , thermodynamics , economic growth , paleontology , biology
A meshless method is presented and analysed. In this approach, one discretises only the boundary, the partial differential equation being solved in the domain by using Taylor series expansion. A least square method is used to apply boundary conditions. In this paper, the method is applied to Navier equations for linear elasticity. Various tests are presented to discuss the efficiency and robustness of the method. The convergence is exponential with respect to the degree but it depends on the radius of convergence of the series. That is why an algorithm has been associated with the Domb–Sykes plot that is a classical method to detect singularities and evaluate the radius of convergence.