Refined beam finite elements for static and dynamic analysis of hull structures

Abstract

The accuracy and reliability of structural analyses are significantly compromised owing to the utilization of simple beam elements to model the global mechanical behaviour of ship hulls. These 1D models entail various assumptions and do not provide accurate and reliable results for hulls with complex structural details, such as cut-outs or reinforcements. The 3D FEM solutions, on the other hand, are computationally expensive. In the present study, refined 1D FE models for the analysis of simplified naval engineering structures have been developed by using the well-known Carrera Unified Formulation (CUF). According to CUF, refined kinematics beam models that go beyond classical theories (Euler, Timoshenko) can be easily developed by expressing the displacement field as an expansion in terms of generic functions, whose form and order are arbitrary. Hence, the stiffness and mass matrices are written in terms of fundamental nuclei, which are independent of the adopted class of beam theory and the FE approximation along the beam axis. As a particular class of CUF models, Lagrange polynomials have been used to formulate beam models at the component scale. According to this approach, each structural component (e.g. hull, longerons, bulkheads, and floors) can be modelled by means of the same 1D formulation. The results clearly demonstrate the enhanced capabilities of the proposed formulation, which is able to replicate solid/shell ANSYS solutions with very low computational efforts.