This paper presents a general procedure to formulate and implement 3D elements of arbitrary order in meshes with multiple element types. This procedure includes obtaining shape functions and integration quadrature and establishing an approach for checking the generated element’s compatibility with adjacent elements’ surfaces. This procedure was implemented in Matlab, using its symbolic and graphics toolbox, and complied as a GUI interface named ShapeGen3D to provide finite element users with a tool to tailor elements according to their analysis needs. ShapeGen3D also outputs files with the element formulation needed to enable users to implement the generated elements in other programming languages or through user elements in commercial finite element software. Currently, finite element (FE) users are limited to employing element formulation available in the literature, commercial software, or existing element libraries. Thus, the developed procedure implemented in ShapeGen3D offers FEM users the possibility to employ elements beyond those readily available. The procedure was tested by generating the formulation for a brick element, a brick transition element, and higher-order hexahedron and tetrahedron elements that can be used in a spectral finite element analysis. The formulation obtained for the 20-node element was in perfect agreement with the formulation available in the literature. In addition, the results showed that the interpolation condition was met for all the generated elements, which provides confidence in the implementation of the process. Researchers and educators can use this procedure to efficiently develop and illustrate three-dimensional elements.

Wave propagation or acoustic emission waves caused by impact load can be simulated using the finite element (FE) method with a refined high-fidelity mesh near the impact location. This paper presents a method to refine a 3D finite element mesh by increasing the polynomial order near the impact location. Transition elements are required for such a refinement operation. Three protocols are defined to implement the transition elements within the low-order FE mesh. Due to the difficulty of formulating shape functions and verification, there are no transition elements beyond order two in the current literature for 3D elements. This paper develops a complete set of transition elements that facilitate the transition from first- to fourth-order Lagrangian elements, which facilitates mesh refinement following the protocols. The shape functions are computed and verified, and the interelement compatibility conditions are checked for each element case. The integration quadratures and shape function derivative matrices are also computed and made readily available for FE users. Finally, two examples are presented to illustrate the applicability of this method.

Finite element (FE) models that simulate wave–superstructure interactions with the coupled Eulerian–Lagrangian (CEL) technique provide a viable and economical solution to estimate wave impact forces on bridge superstructures. One of the main drawbacks of CEL FE models is that they produce solutions distorted by numerical artifacts with very high frequencies that make it difficult to quantify the magnitude of hydrodynamic forces on superstructures. This paper investigated digital filter parameters for horizontal forces extracted from CEL FE models. The optimal filter configuration was evaluated by comparing unfiltered and filtered horizontal force signals with experimentally measured values from a reduced-scale superstructure specimen tested at the O.H. Hinsdale Wave Research Laboratory at Oregon State University. It was found that digital filters with cutoff frequencies below the fundamental frequency of the superstructure produced the best results and that optimizing Eulerian–Lagrangian surface interactions significantly improved the quality of the calculated force signals.

A computationally time-efficient method is introduced to implement pressure load to a Finite element model. Hexahedron elements of the Lagrangian family with Gauss–Lobatto nodes and integration quadrature are utilized, where the integration points follow the same sequence as the nodes. This method calculates the equivalent nodal force due to pressure load using a single Hadamard multiplication. The arithmetic operations of this method are determined, which affirms its computational efficiency. Finally, the method is tested with finite element implementation and observed to increase the runtime ratio compared to the conventional method by over 20 times. This method can benefit the implementation of finite element models in fields where computational time is crucial, such as real-time and cyber–physical testbed implementation.

In structural health monitoring (SHM), finite element models (FEMs) have been used to simulate diverse damage scenarios for training deep learning-based structural damage identification models; however, discrepancies between FEMs and actual structures persist. To bridge this gap, we propose a hierarchical physics-informed domain adaptation (HierPhyDA) approach that synthesizes features from FEMs to mirror those from actual structures and emulates authentic vibration signatures. The proposed solution employs an initial phase of unsupervised anomaly detection using a deep autoencoder approach, followed by a novel physics-informed domain adaptation method that serves as a digital twin of the physical structure. This approach is rigorously evaluated through numerical studies using the ASCE benchmark structure. The results show that the proposed approach outperforms state-of-the-art methods when damage cases from the actual structure are excluded from training and are mutually exclusive from those generated by the FEM.