NBeamAnalysis: Advanced Beam Modeling Framework

• NBeamAnalysis is a comprehensive technical framework offering advanced beam modeling with isogeometric, anisotropic, and nonlinear methods for precise simulation across diverse scientific fields.
• It integrates robust numerical techniques, including rotation-free finite elements, adaptive discretization, and physics-informed neural networks for reliable material and signal identification.
• The framework supports high-throughput analyses in applications such as nonlinear elastodynamics, radio technosignature detection, and neutron beamline simulation, validated by stringent error benchmarks.

NBeamAnalysis is a technical and software framework for the implementation and validation of advanced beam models, finite element formulations, inverse identification, and high-throughput signal and detector analyses in both structural mechanics and astronomical interferometry. The term designates both a collection of principal methodologies (isogeometric, mixed, nonlinear, and anisotropic beam models; advanced contact and damping; material and signal identification workflows) and concrete implementations used in leading research across diverse domains, including nonlinear elastodynamics, radio technosignature detection, beamline simulations, and cosmic beam-pattern discrimination.

1. Advanced Structural Beam Modeling Frameworks

NBeamAnalysis incorporates a range of rigorous beam modeling paradigms:

• Geometrically Exact Isogeometric Bernoulli–Euler and Cosserat Beams: Leveraging isogeometric analysis with NURBS-based discretizations, these models capture full axis curviness, nonlinearity, and objectivity in both planar (Borković et al., 2021) and spatial (Borković et al., 2021) settings. Constitutive models range from exact full-metric (accounting for strong axis curvature and membrane–bending coupling) to hierarchy of reduced models (e.g., Taylor expansions in the curviness parameter), with regime-dependent model selection.
• Anisotropic and Multilayered Beams: The enhanced Timoshenko models resolve stress fields for multilayer beams with arbitrary anisotropy, yielding energetically consistent constitutive relations and revealing explicit coupling of axle (normal) stresses to shear and internal force resultants—effects numerically reaching up to 30% in mid-span stress (Balduzzi et al., 2019).
• Mixed Isogeometric Formulations with Incompatible Strains: Incorporating Cosserat kinematics, extensible directors, and polynomial-based enhanced strains for warping, these models avoid locking and ensure conservation laws while allowing robust condensation of additional degrees of freedom (Choi et al., 19 Jul 2024).

2. Numerical Implementation, Discretization, and Solution Algorithms

NBeamAnalysis codifies best practices in discretization and solution:

• Isogeometric and Rotation-Free Finite Elements: Geometry and kinematic fields are described via high-continuity NURBS or B-spline curves, supporting exact geometry mapping, high accuracy under large displacements, and independence from mesh refinement in cross-sectional warping.
• Adaptive Discretization and Locking Avoidance: Employing B2M1 discretization—using quadratic NURBS for bending, low-order Lagrange (M1) for axial—mitigates membrane locking in large-displacement regimes (Łazorczyk et al., 5 Jun 2025). Reduced integration techniques are standardized for Timoshenko and micropolar beam elements to suppress shear or membrane locking in sandwich and lattice core architectures (Nampally et al., 2019).
• Robust Nonlinear and Modal Solvers: Global Newton–Raphson algorithms, trust-region optimization for inverse problems, and arc-length strategies underpin equilibrium and identification cycles, with convergence measures tailored to beam-specific internal and constraint residuals.
• Time Integration: Implicit energy-momentum consistent schemes guarantee conservation of linear and angular momentum, as well as near-exact energy conservation for nonlinear elastodynamics (Choi et al., 19 Jul 2024), outperforming standard trapezoidal- and midpoint-based timesteppers.

3. Inverse Analysis, Identification, and Machine Learning

NBeamAnalysis supports rigorous material and signal identification:

• Finite Element Model Updating for Heterogeneous Beams: Material fields (Young's modulus, density) are parameterized via low-order meshes independent of the FE or measurement mesh; sensitivity-driven minimization (analytical derivatives for both static and modal data) enables identification of spatially varying properties even under high-experimental noise, with regularization ensuring stability (Łazorczyk et al., 5 Jun 2025).
• Physics-Informed Neural Networks for Nonlocal and Hyperelastic Beams: Mesh-free PINN architectures solve high-order (sixth order) nonlocal eigenproblems with embedded constitutive and boundary constraints, achieving <1% error and efficiently handling broad boundary condition sets (Das et al., 4 Sep 2025). Physics-augmented NN surrogates serve as beam potentials for fast evaluation of hyperelastic, strongly nonlinear (e.g., ring-shaped) cross-sections, guaranteeing thermodynamic and symmetry properties by construction (Schommartz et al., 30 Jun 2024).

4. Signal Processing and Spatial Filtering in Multi-Beam Interferometry

NBeamAnalysis is central to spatial localization and discrimination in large-scale radio astronomical searches:

• Dual-Beam Spatial Filtering: In radio technosignature campaigns, the code ingests millions of Doppler-drifted candidate detections (“hits”) from waterfall spectra, cross-matches them across “on” and “off” synthesized beams, and applies strict spatial localization cuts using SNR ratios and normalized vector dot-products (DOT). Detection confidence follows SNR ratio thresholds (e.g., $R_{\mathrm{SNR}} > \sqrt{N_{\mathrm{ant}}}$) and low DOT scores (strong attenuation/off-beam dissimilarity), reducing the dataset by >99.97% with no recorded false negatives (Sheikh et al., 19 Dec 2025).
• Hierarchical Filtering and Power-Law Scoring: Extending to multi-hour, multi-million-candidate exoplanet (e.g., TRAPPIST-1) searches, NBeamAnalysis layers morphological scoring and empirical power-law cutoffs on SNR/DOT pairs, providing robust RFI rejection and succinct candidate lists for human vetting (Tusay et al., 12 Sep 2024). The pipeline incorporates batch plotting, statistical diagnostics, and integration with upstream search codes (e.g., turboSETI).
• Benchmarking and Validation: Injection-recovery, known-signal validation (e.g., Mars orbiter downlinks), and deterministic control over selection thresholds confirm efficacy across highly dynamic interference conditions.

5. Beamline and Neutron Transport Simulation

NBeamAnalysis is integral to beamline and tracking-intensive physics experiments:

• High-Throughput Neutron Beamline Simulation: The framework incorporates multi-dimensional kernel-based probability sampling, duct source biasing, and full-weighted track outputs for long, shielded neutron beamlines (e.g., NNBAR at ESS) (Holl et al., 2022). All cross-variable correlations (e.g., energy vs. direction) are exactly maintained via weight-correction factors, and performance gains exceed two orders of magnitude over analog sampling.
• Direct Integration with MC Transport Codes: Output couples to MCPL-compatible engines, directly feeding downstream event generators and detector simulations, enabling high-precision, high-statistics modeling of spatial-energy fluxes and multi-order correlations at arbitrary detector locations.

6. Contact, Nonlinearity, and Advanced Effects

NBeamAnalysis includes advanced treatments for beam-beam interactions, nonlinearities, and transient evolution:

• All-Angle Beam Contact (ABC) Formulations: Seamless blending of point-contact (large angles) and line-contact (small angles) regimes with consistent energy-conserving transitions and explicit tangent matrices. Variationally consistent transition functions and octree-based two-stage search algorithms deliver robust, scalable contact search and resolution (Meier et al., 2016).
• Nonlinear Damped, Moving-End, and Multilayer Beam Implementations: Non-cylindrical domain mapping, cubic-Hermite element bases, and Newmark-type schemes ensure stable and accurate simulation of damped Euler–Bernoulli beams with moving boundaries (Quintino et al., 2019) and finite-strain laminated glass beams, where Lagrange-multiplier enforced kinematic compatibility and consistent linearization achieve robust and accurate solutions in modular, multi-physics environments (Zemanová et al., 2013).
• Plasticity and Axial–Bending Fiber Models: Smart adaptive displacement-based elements use iteratively updated section stiffnesses and fiber discretizations to accurately capture strong axial–bending interactions and restoration of strong equilibrium, exhibiting mesh and Gauss point independence in nonlinear RC member simulations (Pantò et al., 2019).

7. Cross-Domain Applicability and Performance

The NBeamAnalysis methodology and software has facilitated research advances across structural mechanics, accelerator beamline optimization, radio astronomy, and material characterization:

• Validated Accuracy and Efficiency: Across applications, error levels against full 2D/3D FE or analytical benchmarks are consistently below 1–5%, with targeted choices of model complexity and reduced forms available for high-throughput regimes.
• Modular, Extensible Infrastructure: Underlying code and process designs, typically in C++ or Python, are modularized (e.g., layer-independence in glass beams, plug-in of neural surrogates), matching the requirements of modern multi-physics simulation and large-sample data science.
• Best Practices in Algorithm Selection and Validation: Recommendations are stratified by regime (e.g., choice of constitutive law given curvature parameterization, adoption of high-order energy-momentum consistent schemes in transient dynamics, or statistical cutoffs in astronomical signal filtering).

NBeamAnalysis, thus, synthesizes rigorous mathematical modeling, state-of-the-art numerical methods, efficient identification and filtering pipelines, and robust validation protocols, enabling comprehensive and scalable analysis in a broad range of beam-related scientific fields.