Adaptive recursive scaled boundary finite element method for forward and inverse interval viscoelastic analysis

Abstract

This paper aims to develop efficient algorithms for both forward and inverse interval viscoelastic analysis. Utilizing an adaptive recursive scaled boundary finite element method (SBFEM), the solution of the forward deterministic solution is approximated using Taylor series expansion, based upon which the interval bounds of displacement/stress can be estimated by interval arithmetic when constitutive parameters are interval variables. On the other hand, the uncertainties of constitutive parameters caused by the uncertain measurements are estimated in terms of their central values and radii, which are identified on the framework of a gradient-based two-stage strategy. At each stage, the process of identification is treated as two deterministic optimization problems that are solved by the Levenberg-Marquardt method.By combining SBFEM with a temporally piecewise adaptive algorithm (TPAA), the proposed method excels in solving singularity and unbounded domain problems with interval uncertainty and in computing intervals of displacements/stresses with stable temporal solution accuracy with different step sizes. Three numerical examples are provided to verify the effectiveness of the proposed approaches, and all the presented results agree well with the references. For the forward interval problem, the bound estimations of stresses near a crack tip and displacements in an unbounded domain are emphasized; for the inverse interval problems, the impacts of initial guesses and locations of measurement points, and regional inhomogeneity are taken into account.