摘要
This paper presents finite element (FE) formulation of the viscoelastic materials described by fractional constitutive law. The time-domain three-dimensional constitutive equation is constructed. The FE equations are set up by treating the fractional operator as a special case of the hereditary integration. The equations are solved by numerical integration method. The numerical algorithm developed by the authors for Liouville-Riemann's fractional derivative was adopted to formulate FE procedures and extended to solve the more general case of the hereditary integration. The numerical examples were given to show the correctness and effectiveness of the integration algorithm.
This paper presents finite element (FE) formulation of the viscoelastic materials described by fractional constitutive law. The time-domain three-dimensional constitutive equation is constructed. The FE equations are set up by treating the fractional operator as a special case of the hereditary integration. The equations are solved by numerical integration method. The numerical algorithm developed by the authors for Liouville-Riemann's fractional derivative was adopted to formulate FE procedures and extended to solve the more general case of the hereditary integration. The numerical examples were given to show the correctness and effectiveness of the integration algorithm.
基金
The project supported by the Ministry of Education of China for the returned overseas Chinese scholars
