Selection of best beam theories based on natural frequencies and dynamic response obtained through mode superposition method

Simplified formulations, particularly 1D models, are fundamental for reducing the computational cost typically required by structural analyses. The use of a limited number of nodal degrees of freedom has inevitable implications for the model’s capabilities and accuracy. Furthermore, the performance of a reduced formulation is strictly problem-dependent, and the choice of a specific set of primary unknowns must be weighted considering their influence on the accuracy of the results of interest. In this work, a procedure for the selection of the best 1D models to adopt for time-response analyses is investigated. Through the Axiomatic/Asymptotic Method (AAM), the influence of single unknowns is evaluated for a specific structural configuration, which can be described as a combination of aspect ratio, material, geometry, and boundary conditions. The finite element governing equations for every considered set of variables are obtained through the Carrera Unified Formulation (CUF). The main indicator for the quality of a theory is based on the evaluation of a certain number of natural frequencies. Dynamic response analyses are then carried out using the modal superposition method to further asses the performance of the selected best theories.