Abstract
In this paper, the generalized finite difference method (GFDM) combined with the implicit Euler method is developed to solve the viscoelastic problem. The mathematical description of the viscoelastic problem is a time-dependent boundary value problem, governed by a second-order partial differential equation and non-linear boundary conditions. To solve the time-dependent differential governing equation and boundary conditions of viscoelasticity, the implicit Euler method and GFDM are employed for the temporal discretization and the spatial discretization respectively. GFDM is a newly developed meshless method, which avoids time-consuming mesh generation and numerical integration. The basic idea of the GFDM originates from the moving least squares method to transform the spatial derivatives at each node into linear summation of nearby node function values with different weighting coefficients. Two numerical examples are presented to illustrate the accuracy, stability and efficiency of GFDM, including the creep and stress relaxation of viscoelastic materials with single connected domains and double connected domains.
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Li, J., Zhang, T. (2021). Generalized Finite Difference Method for Solving Viscoelastic Problems. In: Atluri, S.N., Vušanović, I. (eds) Computational and Experimental Simulations in Engineering. ICCES 2021. Mechanisms and Machine Science, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-67090-0_35
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DOI: https://doi.org/10.1007/978-3-030-67090-0_35
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