Influence of non-structural localized inertia on free vibration response of thin-walled structures by variable kinematic beam formulations

Variable kinematic beam theories are used in this paper to carry out vibration analysis of isotropic thin-walled structures subjected to non-structural localized inertia. Arbitrarily enriched displacement fields for beams are hierarchically obtained by using the Carrera Unified Formulation (CUF). According to CUF, kinematic fields can be formulated either as truncated Taylor-like expansion series of the generalized unknowns or by using only pure translational variables by locally discretizing the beam cross-section through Lagrange polynomials. The resulting theories were, respectively, referred to as TE (Taylor Expansion) and LE (Lagrange Expansion) in recent works. If the finite element method is used, as in the case of the present work, stiffness and mass elemental matrices for both TE and LE beam models can be written in terms of the same fundamental nuclei. The fundamental nucleus of the mass matrix is opportunely modified in this paper in order to account for non-structural localized masses. Several beams are analysed and the results are compared to those from classical beam theories, 2D plate/shell, and 3D solid models from a commercial FEM code. The analyses demonstrate the ineffectiveness of classical theories in dealing with torsional, coupling, and local effects that may occur when localized inertia is considered. Thus the adoption of higher-order beam models is mandatory. The results highlight the efficiency of the proposed models and, in particular, the enhanced capabilities of LE modelling approach, which is able to reproduce solid-like analysis with very low computational costs

Comparison of various 1D, 2D and 3D FE models for the analysis of thin-walled box with transverse ribs subjected to load factors

This paper evaluates various Finite Element (FE) models for the static and dynamic analyses of single- and multi-bay metallic box structures. Load factors are considered in the static response, whereas free vibration analyses are addressed to compare the dynamic performances. Different FE models able to include cross-sectional deformations are compared. These comprise solid (3D) and plate/shell (2D) models, which are obtained by using a general-purpose commercial software. Results related to a hierarchical variable kinematic beam (1D) formulation, which opportunely degenerates into classical beam theories with rigid-cross section assumptions (e.g. Euler-Bernoulli and Timoshenko), are also addressed. Displacements as well as axial and shear stress fields are compared for various loading cases. Regarding dynamic analyses, fundamental and higher-order natural frequencies by various models are computed and the Modal Assurance Criterion is used to compare the eigenmodes. It is concluded that refined models are mandatory to accurately describe the static and dynamic characteristics of thin-walled box structures. Classical and lower-order refined beam models show severe limitations in capturing localized stress/strain fields as well as local mode shapes. Nevertheless, the accuracy of lower-order models is improved as a consequence of the adoption for transverse ribs, which lead to more rigid cross-sections

Influence of non-structural localized inertia on free vibration response of thin-walled structures by variable kinematic beam formulations

Variable kinematic beam theories are used in this paper to carry out vibration analysis of isotropic thin-walled structures subjected to non-structural localized inertia. Arbitrarily enriched displacement fields for beams are hierarchically obtained by using the Carrera Unified Formulation (CUF). According to CUF, kinematic fields can be formulated either as truncated Taylor-like expansion series of the generalized unknowns or by using only pure translational variables by locally discretizing the beam cross-section through Lagrange polynomials. The resulting theories were, respectively, referred to as TE (Taylor Expansion) and LE (Lagrange Expansion) in recent works. If the finite element method is used, as in the case of the present work, stiffness and mass elemental matrices for both TE and LE beam models can be written in terms of the same fundamental nuclei. The fundamental nucleus of the mass matrix is opportunely modified in this paper in order to account for non-structural localized masses. Several beams are analysed and the results are compared to those from classical beam theories, 2D plate/shell, and 3D solid models from a commercial FEM code. The analyses demonstrate the ineffectiveness of classical theories in dealing with torsional, coupling, and local effects that may occur when localized inertia is considered. Thus the adoption of higher-order beam models is mandatory. The results highlight the efficiency of the proposed models and, in particular, the enhanced capabilities of LE modelling approach, which is able to reproduce solid-like analysis with very low computational costs