Non-conventional 1D and 2D finite elements based on CUF for the analysis of non-orthogonal geometries

Abstract

When dealing with innovative materials – such as composites and metamaterials with complex microstructure – or structural components with non-orthogonal beam/plate geometry, the Finite Element Method can become very costly in calculations and time because of the use of very fine 3D meshes. By exploiting the Node-Dependent Kinematic approach of the Carrera Unified Formulation and using Lagrange expanding functions, this work presents the implementation of non-conventional 1D and 2D elements mainly based on the 3D integration of the approximating functions and computation of 3D Jacobian matrix inside the element for the derivation of stiffness and mass matrices; substantially, the resulting elements are 3D elements in which the order of expansion can be different in the three spatial directions. The free vibration analysis of some typical components is performed and the results are provided in terms of natural frequencies. The present elements allow us to accurately study beam-like and plate-like structures with non-orthogonal geometries by employing much less degrees of freedom with respect to the use of classical 3D finite elements.