The numerical analysis formulation of the viscoelastic solid modeled by fractional operator
分数算子描述的黏弹性体力学问题数值方法

The numerical method of mechanical problems for the viscoelastic solids with Riemann-Liouville fractional derivative model is presented in this paper. Instead of using finite Grunwald definition of fractional derivative to approximate the Riemann-Liouville's, this work has developed a numerical algorithm directly from Riemann-Liouville's definition by taking advantages of the features of its integrand kernel, assuming the approximating function for the integrand and making use of Newmark-type numerical methods. The numerical formulations are used to analyze the transient dynamic response for a viscoelastic oscillator and the finite element analysis procedures. The sample results show that the proposed method possesses the advantages of fast convergence, higher accuracy, higher stability and easy for application and further modification.