A fast global nodewise mass matrix inversion framework tailored for sparse block-diagonal systems

Abstract

The present work aims to elucidate the benefits of high-order layerwise mechanics in explicit dynamic and eigen frequency problems applicable to thin-walled structures. High order layerwise mechanics are mainly used for the solution of linear and non-linear static problems due to their ability to predict accurately the strain and stress fields. The increased accuracy of high order layerwise mechanics is attributed to the coupling between rotational–translational​ degrees of freedom; but simultaneously consists their major drawback when it comes to the formulation of the mass matrix. That is, while the 2D and 3D continuum elements can form diagonal mass matrices, which are easily inverted, in the case of high order layerwise elements block-diagonal mass matrices are formulated due to the coupling of the degrees of freedom. Even if the sparsity of block-diagonal matrices is large, the solution time of explicit dynamics and eigen frequency problems is significantly increased. The present work aims to alleviate this issue by proposing an efficient numerical framework, adopting a global nodewise mass matrix inversion procedure which relies on the block-diagonal nature of the matrix, attained by exploiting the Gauss–Lobatto–Legendrequadrature. Applications of sandwich structures are considered and multiphysics explicit dynamics and modal analyses are conducted exploiting the proposed mass inversion methodology by accelerating the solution procedure in computationally demanding problems focused on thin-walled structures made of different materials through the thickness by incorporating high order layerwise mechanics.