Development of Finite Element Models With Node-Wise Variations of Structural Theories for Dynamic Analyses

Abstract This paper introduces a novel modeling approach to enhance the accuracy and computational efficiency of Finite Element (FE) models for structural dynamics. The approach incorporates three key features: 2D elements, higher-order structural theories, and a node-dependent kinematics (NDK) framework where each FE node can have a distinct set of degrees of freedom. Built on the Carrera Unified Formulation (CUF), this framework enables the development of any structural theory and its corresponding governing equations and FE arrays. The NDK approach allows structural theory to vary across nodes, creating a global-local scheme that combines high-fidelity local models with low-fidelity regions to optimize computational efficiency. This work focuses on free-vibration analyses of shell structures for aerospace applications and the effect of higher-order models on the natural frequencies and modal shapes. Two results are presented: the best global structural theory for a given problem and the best local distributions of high-fidelity models, i.e., models in which the computational cost is minimized for a given accuracy threshold. In previous works, a penalization technique was employed to develop specific models. In contrast, this paper introduces a new approach to constructing finite element matrices by retrieving each node’s active degrees of freedom. The results indicate the most effective generalized unknown variables for building reduced models with optimized computational overhead.