Combining shell and GBT-based finite elements: Vibration and dynamic analysis

Abstract

This paper extends the approach previously proposed by the authors Manta et al. (2020, 2021) to the dynamic case, more precisely to the calculation of natural frequencies (including pre-loaded members) and the linear time-history response of thin-walled members and frames with complex geometry, undergoing global–local–distortional deformation. This approach relies on a combination of standard shell and GBT-based (beam) finite elements, where the prismatic beam parts are modelled with standard GBT-based elements with a minimum number of deformation modes (hence a minimum number of DOFs), while the geometrically complex zones (perforations, tapering, joints) are handled using shell elements. Three numerical examples are presented to demonstrate the capabilities and potential of the proposed approach. These examples concern (i) a lipped channel cantilever with two long holes, (ii) a lipped channel cantilever with a tapered segment, subjected to pre-loading, and (iii) an L-shaped frame with I-section members and a tapered joint. For comparison and validation purposes, full shell finite element model solutions are provided. In all examples, it is concluded that the proposed approach leads to very accurate results and a significant DOF economy with respect to full shell finite element models.