Abstract The scaled boundary finite element method is a semi-analytical method that only needs to mesh on the boundary without fundamental solution, which makes it powerful to deal with singular and unbounded problem. This paper aims to propose a second order sensitivity analysis method for the scaled boundary finite element method, which can calculate the second order gradients of the responses with respect to the parameters accurately and efficiently. An improved first order sensitivity analysis method is presented through establishing a new Hamilton eigenproblem equation with only right eigenvectors. The second order Hamilton eigenproblem equation is constructed and the semi-analytical sensitivities of displacements and stresses are further obtained by a series of differential equation. The proposed method is then applied to the shape sensitivity analysis of linear cracked structures and corresponding uncertainty propagation analysis. Finally, two numerical examples are investigated to demonstrate the validity of the proposed method.
Received: 04 September 2014
Published: 28 February 2014