Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination

This paper proposes a parallel direct solution of flexible multibody systems based on block Gaussian elimination. The Craig–Bampton method is utilized to model flexible bodies within the multibody system, resulting in a reduction in the size of the system equations. To address the time integration problem, an implicit stiff scheme is adopted to obtain large time step sizes. When forming the linearized systemic equations, global sparsity in the Jacobian matrix and similar local sparsity in submatrices can be observed. Subsequently, block Gaussian elimination is introduced for the direct solution of these linearized equations. The algorithm is designed to be parallelizable at the algorithm level, with a specific processing order for the submatrices of the constraints. The stability of the method is guaranteed by the positive definite and symmetric properties in the diagonal matrices in the Craig–Bampton method. The parallel efficiency and numerical stability of the method are confirmed through numerical examples in homemade codes parallelized by OpenMP.