Solving Viscoelastic Problems Using Complex Fourier Boundary Element Method

A complex Fourier boundary element method for two-dimensional numerical analysis of viscoelastic materials such as rubber, concrete, polymers, or biological substances using radial basis functions (RBF) is proposed in the current paper. This matter was considered due to the fact that the demand for a much more realistic vision is increasing as science proceeds towards optimized approaches. The classic reciprocal work theorem is reconsidered in the well-known boundary element method (BEM) when complex Fourier RBFs serve as shape functions instead of the customary ones. These functions can satisfy various areas such as exponential and trigonometric fields as well as polynomial fields. Afterwards, displacements and tractions are approximated and compared to both Lagrangian and analytical procedures for three benchmark problems to determine the validity and stability of the proposed method. The results show magnificent accuracy and efficiency for the Fourier method in comparison with the classic approach, and by considering the fact that more accurate results are gained while incorporating fewer degrees of freedom in the analysis procedure, it was concluded that the suggested method is both economical and more efficient.