Hierarchical Composite Grid Method for Global-Local Analysis of Laminated Composite Shells

A hierarchical version of the composite grid method (denoted as HFAC), which exploits the solution of the shell model in studying local effects via 3D solid model, is developed. Convergence studies on a beam/2D model problem indicate that the spectral radius of the point iteration matrix for the HFAC method is and with exact and approximate auxiliary coarse grid solutions, respectively, where L and H are the span and the thickness of the beam, respectively. Numerical experiments in multidimensions confirm these findings. 1.0 Introduction Global-local techniques for laminated composite shells, which merge the Equivalent Single Layer (ESL) model aimed at predicting overall response with Discrete Layer (DL) model intended for capturing local effects, are recently receiving an increasing attention. We refer to [22] for a comprehensive review of global-local techniques for composite laminates and to [7] and [8] for various aspects of reliability, convergence and accuracy of global-local techniques. In this paper, we are focusing only on the class of global-local techniques that advocates a hierarchical solution strategy in the sense that information from the analysis of an ESL model is exploited in the resolution of local effects using a DL model. Among the most popular hierarchical global-local strategies are the various forms of multigrid and composite grid methods [14]-[19], [30] as well as the methods based on hierarchical decomposition of approximation space [1]-[6], [20]-[22]. Recently, the composite grid method originated for displacement-based linear systems, has been extended to hybrid systems [26]. Engineering global-local approaches, which approximate a detailed response by means of post processing techniques, such as subjecting refined discrete layer model to the boundary conditions extracted from the global ESL model, can be viewed as O 1 ( ) O L H ⁄ ( ) ( )