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.

当处理具有创新性的材料（例如具有复杂微观结构的复合材料和超材料）或具有非正交梁/板几何结构的结构部件时，由于使用了非常精细的3D网格，有限元方法在计算和时间上会变得非常昂贵。通过利用Carrera统一公式的依赖于节点的运动学方法并使用Lagrange扩展函数，该工作主要基于逼近函数的3D集成和内部3D Jacobian矩阵的计算，提出了非常规1D和2D元素的实现。用于推导刚度和质量矩阵的元素；基本上，所得元素是3D元素，其中在三个空间方向上的扩展顺序可能不同。这进行了一些典型组件的自由振动分析，并以固有频率提供了结果。通过使用相对于经典3D有限元要少得多的自由度，本单元使我们能够准确地研究具有非正交几何形状的梁状和板状结构。