Sensitivity analysis of the scaled boundary finite element method for elastostatics

As a semi-analytical structural analysis algorithm, the scaled boundary finite-element method (SBFEM) only discretizes the boundary of the analyzed domain without the need of fundamental solutions, which makes it powerful for problems with stress singularity or unbounded foundation media. In this paper, a sensitivity analysis method of SBFEM is proposed for elastostatics, through which the first order derivatives of the structural responses with respect to the design parameters can be obtained efficiently and accurately. An approach is suggested to compute the eigenvalue and eigenvector sensitivities of the Hamilton matrix, which are then used to calculate the analytical derivative of the stiffness matrix. Based on these calculations, the sensitivities of displacements and stresses are further obtained by a series of differential equations. The proposed sensitivity analysis method is also applied to the fracture mechanics problems. Three numerical examples are investigated to demonstrate the validity of the proposed method.