An interpolating element free Galerkin scaled boundary method for elastostatic sensitivity analysis

Abstract

To enable efficient and accurate first-order derivative computations of structural responses with respect to design parameters, this paper proposes a semi-analytical approach termed the interpolating element-free Galerkin scaled boundary method (IEFG-SBM) for elastostatic sensitivity analysis. Discretizing only the boundary with scattered nodes and avoiding the need for fundamental solutions, this method eliminates element connectivity requirements and proves particularly effective for problems involving stress singularities or unbounded domains. The shape functions derived from the improved interpolating moving least-squares (IIMLS) method satisfy the delta function property, allowing essential boundary conditions to be imposed exactly without additional treatment. In the sensitivity formulation, the derivatives of the eigenvalues and eigenvectors of the Hamilton matrix are computed analytically to obtain the stiffness matrix derivative, requiring only the right eigenvectors and thereby substantially reducing both computational cost and memory usage. The resulting stiffness derivatives are subsequently incorporated into a set of differential equations, the solution of which yields displacement and stress sensitivities. The performance of the proposed method is validated through several numerical examples, demonstrating satisfactory accuracy and computational robustness.