Fast algorithm for structural dynamics problems using differential quadrature method and $${\varvec{V}}$$ V -transformation

Abstract

The differential quadrature method (DQM) has been widely used for structural dynamics problems computation. Traditional DQM usually adopts simultaneous discretization in multi-grid points, and then all variables are solved simultaneously. Obviously, this will result in the curse of dimensionality problem for large-scale systems. In this paper, on the basis of the multi-stage high-order time domain DQM, a fast numerical calculation method for large-scale structural dynamics problems based on $${\varvec{V}}$$ -transformation is proposed. Using the $${\varvec{V}}$$ -transformation possessed by the weighting coefficient matrix of DQM, the whole Jacobian matrix equations involved in the traditional approach of DQM can be decoupled into blocks; thus, the multi-stage block recursive method is derived. Numerical experiments show that: even using 2s times step size of the Newmark method, the computational accuracy of DQM is about 2–3 orders of magnitude higher than that of the Newmark method. Furthermore, three different scale systems are used for time test and the results show that the multi-stage block recursive method can obtain high speedup ratio, which can significantly improve the computational efficiency of large-scale structural dynamics problems.