An element-free Galerkin approach for rigid–flexible coupling dynamics in 2D state

Abstract

Based on an improved element-free Galerkin (EFG) method and the geometric nonlinear elastic theory, an element-free numerical approach for rigid–flexible coupling dynamics of a rotating hub–beam system is implemented. Using the Hamilton principle, the coupled nonlinear integral-differential governing equations are derived, in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement. By the EFG method where the global interpolating moving least squares (IMLS) and generalized moving least squares (IGMLS) were used for discretizing the longitudinal and transverse deformation variables, respectively, the spatially element-free discretized dynamic equations of the system are obtained and the Newmark scheme was selected as the time integration method for the numerical computation. The superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions. The transverse bending vibration and structural dynamics of the flexible beam in non-inertial system are analyzed in the numerical simulations and influence parameters of the EFG method are also fully discussed. Simulation results verify the feasibility of the improved EFG approach for rigid–flexible coupling dynamics.