A SBFEM and sensitivity analysis based algorithm for solving inverse viscoelastic problems

Abstract

A new numerical algorithm to solve inverse viscoelastic problems of identification is presented. By expanding variables within a discretized time interval, a temporally and spatially coupled viscoelastic problem is decoupled into a series of recursive spatial problems which are solved by Scaled Boundary Finite Element Method (SBFEM). The computing accuracy of displacement and its derivative with respect to constitutive parameters can be guaranteed via a recursive self-adaptive process, providing a reliable platform for gradient based inverse analysis. A two step strategy cooperating with the Levenberg–Marquardt method is proposed to solve inverse problems of parameters identification. Numerical examples, with homogeneous and regional inhomogeneous cases, are provided to verify proposed approaches, and the impacts of initial guess, measurement points, and noisy data on the result are taken into account.