Expanding element interpolation method for analysis of thin-walled structures

An expanding element is obtained by adding virtual nodes along the perimeter of the traditional discontinuous element. There are two kinds of shape functions in the expanding element: (i) the raw shape function, i.e. shape function of the original discontinuous element, involving only inner nodes; (ii) the fine shape function, which involves all the nodes including inner nodes and the newly added virtual nodes. The polynomial order of fine shape functions of the expanding elements increases by two compared with their corresponding raw shape functions. In this paper, we apply the expanding element interpolation method to analysis of thin-walled structures. An adaptive element subdivision method for evaluating nearly singular integrals is proposed. Numerical results have demonstrated that our method has high level of accuracy and is able to analyze very slender structures with the aspect ratio up to 1e6.