Fractional modelling and numerical simulations of variable-section viscoelastic arches

作者：

Highlights：

• The fractional governing equations of three variable section viscoelastic arches are established based on two fractional viscoelastic constitutive models.

• Numerical solutions of displacement, stress and strain are obtained directly in the time domain by shifted Chebyshev polynomial algorithm.

• Convergence analysis and error estimation prove the high accuracy and efficiency of proposed algorithm.

• Performance testing for variable-section arches with different viscoelastic materials.

摘要

•The fractional governing equations of three variable section viscoelastic arches are established based on two fractional viscoelastic constitutive models.•Numerical solutions of displacement, stress and strain are obtained directly in the time domain by shifted Chebyshev polynomial algorithm.•Convergence analysis and error estimation prove the high accuracy and efficiency of proposed algorithm.•Performance testing for variable-section arches with different viscoelastic materials.

论文关键词：Viscoelastic arches,Nonlinear fractional integro-differential equations,Shifted Chebyshev polynomial algorithm,Numerical solutions,Fractional constitutive models

论文评审过程：Received 1 January 2021, Revised 21 April 2021, Accepted 12 May 2021, Available online 1 June 2021, Version of Record 1 June 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126376