An efficient parallel algorithm for flexible multibody systems based on domain decomposition method

Recently, a large number of lightweight flexible structures are successfully used in the field of aerospace industry, intelligent robot and 3D printing. Because of the increasing flexibility of elastic components, some large scale mechanical systems will perform typical rigid-flexible coupled dynamic characteristic. Previous studies have indicated that the traditional modeling methods of the flexible multibody system based on the assumptions of small rotations and small deformation, such as the floating frame of reference method, can not lead to correct results for the dynamic response of those large deformation structures. Under the framework of Isogeometric analysis, the basis functions of the NURBS are employed to discretize the displacement field of elastic components with large deformation. Based on the large deformation theory of the continuum mechanics, the geometrical nonlinearity of planar structures undergoing the overall motion and large deformation is accurately taken into account. In order to improve the computational efficiency, some efficient formulations to calculate the elastic force and the tangent stiffness matrix are proposed via the invariant matrix method. Furthermore, based on the finite element tearing and interconnecting (FETI) method, an efficient parallel algorithm is presented to deal with the dynamic equations of motion for flexible multibody systems. First, the governing partial differential equations of multibody systems are transformed into a set of nonlinear algebraic equations after spatial and time discretization. Then, the preconditioned conjugate gradient method is exploited to solve the linearization equation in parallel. Compared with the existing parallel direct methods for flexible multibody systems, the proposed method can improve the computational efficiency significantly. Finally, several numerical examples are given to validate the effectiveness of the proposed parallel algorithm, including the complexity, the speed-up ratio and the scalability.