A Temporally Piecewise Adaptive Scaled Boundary Finite Element Method for Solving the Fuzzy Uncertain Viscoelastic Problems
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The numerical solutions for uncertain viscoelastic problems have important theoretical and practical significance. The paper develops a new approach by combining the scaled boundary finite element method (SBFEM) and fuzzy arithmetic. For the viscoelastic problems with zero uncertainty, the SBFEM and the temporally piecewise adaptive algorithm is employed in the space domain and the time domain, respectively, in order to provide an accurate semi-analytical boundary-based approach and to ensure the accuracy of discretization in the time domain with different sizes of time step at the same time. The fuzzy arithmetic is used to address the uncertainty analysis of viscoelastic material parameters, and the transformation method is used for computation with the advantages of effectively avoiding overestimation and reducing the computational costs. Numerical examples are provided to test the performance of the proposed method. By comparing with the analytical solutions and the Monte Carlo method, satisfactory results are achieved.
KeywordsViscoelasticity Uncertainty Scaled boundary finite element Fuzzy arithmetic
The research leading to this paper is funded by NSF [11572077, 11202046, 10802015], NKBRSF [2015CB057804], Natural Science Funding of Liaoning Province [2015020141, 2015020119] and the Fundamental Research Funds for Central Universities [DUT17LK11, DUT17ZD311].
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