Development of 1D Finite Elements With Node-Wise Higher-Order Structural Theories

This paper presents an innovative modeling approach to increase the accuracy and computational efficiency of Finite Element (FE) models. The present method integrates three key advancements: (1) one-dimensional elements, (2) higher-order structural theories, and (3) a node-dependent kinematics (NDK) framework, where each FE node can possess an independent set of degrees of freedom. Based on the Carrera Unified Formulation (CUF), this framework facilitates the derivation of arbitrary structural theories along with their governing equations and FE arrays. The NDK approach enables spatially varying structural theories. The study focuses on free vibration analyses of civil engineering beam structures. This work identifies the most efficient spatial distributions of high-fidelity models—those that minimize computational cost while meeting a predefined accuracy threshold. This paper proposes a novel methodology for constructing finite element matrices by dynamically retrieving the active degrees of freedom at each node. The results demonstrate the optimal selection of generalized unknown variables.