Fiber-reinforced polymers (FRPs) retrofit reinforced concrete (RC) structures. ABAQUS finite element software was used to perform numerical parametric analysis on a group of RC beams in this research. All specimens were retrofitted by FRP strips as an external retrofitting and experimentally tested up to previous researchers’ failure points. The range of subjects examined in these RC beams included cracking torque, ultimate torque, angle of twist, and the effect of using FRP on these subjects. We applied artificial neural networks (ANNs) to predict the structural behavior of RC beams under combined torsion and bending to develop the research accuracy. After testing, the ANN results were compared with the ABAQUS results. Consequently, a reasonable examination of the determined mathematical and trial results confirmed this study’s logical accuracy in predicting retrofitted RC beams’ structural behavior under combined loading.

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of the algorithm, and show that the theoretical results also are applied to weak Galerkin (WG) methods. The main features of our analysis are twofold: one is that we only need the minimal regularity of the model problem; the other is that we do not require the triangulations to be quasi-uniform. Numerical experiments are provided to confirm the theoretical results.

Structural dynamics analysis is essential for predicting the behavior of engineering systems under dynamic forces. This study presents a hybrid framework that combines analytical modeling, machine learning, and optimization techniques to enhance the accuracy and efficiency of dynamic response predictions for Single-Degree-of-Freedom (SDOF) systems subjected to harmonic excitation. Utilizing a classical spring–mass–damper model, Fourier decomposition is applied to derive transient and steady-state responses, highlighting the effects of damping, resonance, and excitation frequency. To overcome the uncertainties and limitations of traditional models, Extended Kalman Filters (EKFs) and Physics-Informed Neural Networks (PINNs) are incorporated, enabling precise parameter estimation even with sparse and noisy measurements. This paper uses Adam followed by LBFGS to improve accuracy while limiting runtime. Numerical experiments using 1000 time samples with a 0.01 s sampling interval demonstrate that the proposed PINN model achieves a displacement MSE of 0.0328, while the Eurocode 8 response-spectrum estimation yields 0.047, illustrating improved predictive performance under noisy conditions and biased initial guesses. Although the present study focuses on a linear SDOF system under harmonic excitation, it establishes a conceptual foundation for adaptive dynamic modeling that can be extended to performance-based seismic design and to future calibration of Eurocode 8. The harmonic framework isolates the fundamental mechanisms of amplitude modulation and damping adaptation, providing a controlled environment for validating the proposed PINN–EKF approach before its application to transient seismic inputs. Controlled-variable analyses further demonstrate that key dynamic parameters can be estimated with relative errors below 1%—specifically 0.985% for damping, 0.391% for excitation amplitude, and 0.692% for excitation frequency—highlighting suitability for real-time diagnostics, vibration-sensitive infrastructure, and data-driven design optimization. This research deepens our understanding of vibratory behavior and supports future developments in smart monitoring, adaptive control, resilient design, and structural code modernization.

The embedded discontinuous Galerkin (EDG) method by Cockburn, Gopalakrishnan and Lazarov [B. Cockburn, J. Gopalakrishnan and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second-order elliptic problems, SIAM J. Numer. Anal. 47 2009, 2, 1319–1365] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from discontinuous functions to continuous ones, and adopts piecewise polynomials of equal degrees on simplex meshes for all variables. In this paper, we analyze a new EDG method for second-order elliptic problems on polygonal/polyhedral meshes. By using piecewise polynomials of degrees k + 1 {k+1} , k + 1 {k+1} , k ( k ≥ 0 {k\geq 0} ) to approximate the potential, numerical trace and flux, respectively, the new method is shown to yield optimal convergence rates for both the potential and flux approximations. Numerical experiments are provided to confirm the theoretical results.

For interval-valued intuitionistic fuzzy sets featuring complementary symmetry in evaluation relations, this paper proposes a novel, complete fuzzy multi-attribute group decision-making (MAGDM) method that optimizes both expert weights and attribute weights. First, an optimization model is constructed to determine expert weights by minimizing the cumulative difference between individual evaluations and the overall consistent evaluations derived from all experts. Second, based on the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), the improved closeness index for evaluating each alternative is obtained. Finally, leveraging entropy theory, a concise and interpretable optimization model is established to determine the attribute weight. This weight is then incorporated into the closeness index to enable the ranking of alternatives. Integrating these features, the complete fuzzy MAGDM algorithm is formulated, effectively combining the strengths of subjective and objective weighting approaches. To conclude, the feasibility and effectiveness of the proposed method are thoroughly verified and compared through detailed examination of two real-world cases.

In the midst of the neural network’s success in solving partial differential equations, tackling eigenvalue problems using neural networks remains a challenging task. However, the Physics Constrained-General Inverse Power Method Neural Network (PC-GIPMNN) approach was proposed and successfully applied to solve the single-group critical problems in reactor physics. This paper aims to solve critical problems in multi-group scenarios and in more complex geometries. Hence, inspired by the merits of traditional source iterative method, which can overcome the ill-condition of the right side of the equations effectively and solve the multi-group problem effectively, we propose two residual loss function called Decoupling Residual loss function and Direct Iterative loss function. Our loss function can deal with multi-group eigenvalue problem, and also single-group eigenvalue problem. Using the new residual loss functions, our study solves one-dimensional, two-dimensional, and three-dimensional multi-group problems in nuclear reactor physics without prior data. In numerical experiments, our approach demonstrates superior generalization capabilities compared to previous work.