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1. Convergence Characteristics of Geometrically Accurate Spatial Finite Elements

   https://doi.org/10.1115/1.4048731  

   Tinsley, Brian; Shabana, Ahmed A. (January 2021, Journal of Computational and Nonlinear Dynamics)

   null (Ed.)

   Abstract The convergence characteristics of three geometrically accurate spatial finite elements (FEs) are examined in this study using an eigenvalue analysis. The spatial beam, plate, and solid elements considered in this investigation are suited for both structural and multibody system (MBS) applications. These spatial elements are based on geometry derived from the kinematic description of the absolute nodal coordinate formulation (ANCF). In order to allow for an accurate reference-configuration geometry description, the element shape functions are formulated using constant geometry coefficients defined using the position-vector gradients in the reference configuration. The change in the position-vector gradients is used to define a velocity transformation matrix that leads to constant element inertia and stiffness matrices in the case of infinitesimal rotations. In contrast to conventional structural finite elements, the elements considered in this study can be used to describe the initial geometry with the same degree of accuracy as B-spline and nonuniform rational B-spline (NURBS) representations, widely used in the computer-aided design (CAD). An eigenvalue analysis is performed to evaluate the element convergence characteristics in the case of different geometries, including straight, tapered, and curved configurations. The frequencies obtained are compared with those obtained using a commercial FE software and analytical solutions. The stiffness matrix is obtained using both the general continuum mechanics (GCM) approach and the newly proposed strain split method (SSM) in order to investigate its effectiveness as a locking alleviation technique. 

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2. High order weight‐adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes

   https://doi.org/10.1002/nme.6823  

   Guo, Kaihang; Chan, Jesse (September 2021, International Journal for Numerical Methods in Engineering)

   Abstract This article presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian–Eulerian formulation to map the wave equation from a time‐dependent moving physical domain onto a fixed reference domain. For moving curved meshes, weighted mass matrices must be assembled and inverted at each time step when using explicit time‐stepping methods. We avoid this step by utilizing an easily invertible weight‐adjusted approximation. The resulting semi‐discrete weight‐adjusted DG scheme is provably energy stable up to a term that (for a fixed time interval) converges to zero with the same rate as the optimal error estimate. Numerical experiments using both polynomial and B‐spline bases verify the high order accuracy and energy stability of proposed methods. 

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3. A vectorial envelope Maxwell formulation for electromagnetic waveguides with application to nonlinear fiber optics

   https://doi.org/10.1016/j.camwa.2025.05.026  

   Henneking, Stefan; Grosek, Jacob; Demkowicz, Leszek (September 2025, Computers & Mathematics with Applications)

   This article presents an ultraweak discontinuous Petrov-Galerkin (DPG) formulation of the time-harmonic Maxwell equations for the vectorial envelope of the electromagnetic field in a weakly-guiding multi-mode fiber waveguide. This formulation is derived using an envelope ansatz for the vector-valued electric and magnetic field components, factoring out an oscillatory term of exp(-ikz) with a user-defined wavenumber k, where z is the longitudinal fiber axis and field propagation direction. The resulting formulation is a modified system of the time-harmonic Maxwell equations for the vectorial envelope of the propagating field. This envelope is less oscillatory in the z-direction than the original field, so that it can be more efficiently discretized and computed, enabling solutions to the vectorial DPG Maxwell system in fibers that are 1000x longer than previously possible. Different approaches for incorporating a perfectly matched layer for absorbing the outgoing wave modes at the fiber end are derived and compared numerically. The resulting formulation is used to solve a 3D Maxwell model of an ytterbium-doped active gain fiber amplifier, coupled with the heat equation for including thermal effects. The nonlinear model is then used to simulate thermally-induced transverse mode instability (TMI). The numerical experiments demonstrate that it is computationally feasible to perform simulations and analysis of real-length optical fiber laser amplifiers using discretizations of the full vectorial time-harmonic Maxwell equations. The approach promises a new high-fidelity methodology for analyzing TMI in high-power fiber laser systems and is extendable to including other nonlinearities. 

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4. Triangular cross-section beam splitters in silicon carbide for quantum information processing

   https://doi.org/10.1557/s43579-024-00557-0  

   Majety, Sridhar; Saha, Pranta; Kekula, Zbynka; Dhuey, Scott; Radulaski, Marina (May 2024, MRS Communications)

   Abstract Triangular cross-section color center photonics in silicon carbide is a leading candidate for scalable implementation of quantum hardware. Within this geometry, we model low-loss beam splitters for applications in key quantum optical operations such as entanglement and single-photon interferometry. We consider triangular cross-section single-mode waveguides for the design of a directional coupler. We optimize parameters for a 50:50 beam splitter. Finally, we test the experimental feasibility of the designs by fabricating triangular waveguides in an ion beam etching process and identify suitable designs for short-term implementation. 

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5. Strengthening Architected Instability-Based Metamaterials (AIMs)

   https://doi.org/10.1115/SSDM2025-152066  

   Wan, Li; Young, Devin; Zhang, Yunlan (May 2025, American Society of Mechanical Engineers)

   Abstract Architected Instability-based Metamaterials (AIMs) composed of curved beams can exhibit multi-stable geometric phase transformations. By tailoring geometry and topology, AIMs can accommodate large reversible deformations while dissipating energy beyond the capabilities of conventional materials. These exceptional mechanical properties are attractive for aerospace engineering applications, including energy-absorbing components in landing gears, impact-resistant protective structures, and vibration-damping systems. Nevertheless, this very mechanism that enables reversible energy dissipation also limits its capacity, because geometric phase transformations like snap-through buckling occur at low specific strength. Thus, the reversible energy dissipation capability cannot be easily leveraged in aerospace applications. In this work, we propose a theoretical and numerical modeling integrated approach to manipulate the out-of-plane stiffness distribution of curved beams. Compared to the conventional AIMs with uniform curved beams, the strength of the proposed beam configuration can be largely improved, while the local maximum strain remained relatively lower during phase transformations. Finite element analysis and experiments show this approach mitigates the local strain concentration effects of AIMs. Without inducing unreversible plastic deformation, the mechanical properties like the maximum peak strength, trapped energy during compression, and energy dissipation under cyclic loading can be increased by 62.1%, 82.5%, and 45.6%, respectively. 

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