Surrogate Model Based Numerical Solutions For Direct/Inverse Fractional Viscoelastic/Bimodular Problems

In the process of solving an inverse/optimization problem numerically, its corresponding direct problem usually needs to be solved repeatedly. For the case where sensitivity analysis is difficult to implement, the number of solving direct problems will be greatly increased if a non-sensitivity analysis based algorithm, such as the intelligent algorithm, is adopted. Thereby, how to efficiently solve the direct problem is an important issue taken into account for improving the computational efficiency of solving inverse/optimization problems.This thesis focuses on two problems with the difficulty of sensitivity analysis, i.e. fractional viscoelastic problem and bimodular problem. In order to reduce the computational expense on solving direct problems, two surrogate technique based approximate numerical models to solve direct problems are presented, resulting in a significant increase of computational efficiency of solving inverse problems.The major achievements include1. An approximate numerical model to solve homogeneous/regionally inhomogeneous direct fractional viscoelastic problems is presented using the Kriging surrogate technique. In order to reduce the computational expense on time domain, three strategies are proposed in the modeling process. Compared with the original FE/FE-FD model, the approximate model’s computational expense on a single time to solve the direct problem is drastically reduced. A gridding partition based continuous ant colony algorithm is employed to identify viscoelastic constitutive parameters. Numerical verifications indicate that a great amount of computational cost on solving inverse fractional viscoelastic problems can be saved with sufficient computing accuracy.2. An approximate numerical model to solve homogeneous/regionally inhomogeneous direct bimodular problem is presented using the Kriging surrogate technique. Compared with the original FE model, the approximate model’s computational expense on a single time to solve the direct problem is drastically reduced. A gridding partition based continuous ant colony algorithm is employed to identify bimodular constitutive parameters. Numerical verifications indicate that a great amount of computational cost on solving inverse bimodular problems can be saved with sufficient computing accuracy.3. For further improving the computational efficiency, a sensitivity analysis based numerical model to solve the2-D direct bimudular problem and a two level sensitivity analysis based numerical model to solve the2-D inverse bimudular problem are proposed, respectively. The formulae to calculate sensitivity are derived. The Newton-Raphson method and Gauss-Newton method are employed to solve the direct and inverse bimudular problems, respectively. Numerical verifications indicate that the computational efficiency of solving the direct/inverse bimudular problems is significantly improved using these models in comparison with the non-sensitivity analysis based algorithms presented in this paper.A number of numerical examples are provided to verify the proposed numerical algorithms, and several factors related to the computing accuracy and efficiency are discussed.