A Unified Corotational Framework for 2D Beams: Bridging the Crisfield and Krenk Formulations

Thu, 08 Oct 2026 00:00:00 +0200

This paper presentes a unified corotational framework for 2D beam elements that achieves a theoretical synthesis between the seminal formulations of Crisfield and Krenk. A central contribution of this research is the analytical demonstration that these two traditionally distinct approaches converge to an identical tangent stiffness matrix, offering a unified perspective on objective corotational kinematics. The framework is systematically applied to three fundamental kinematic theories: Euler-Bernoulli, Timoshenko, and shallow arch Euler-Bernoulli, demonstrating its versatility across different levels of structural refinement. By decomposing the motion into a global rigid-body component and a local deformational part, characterized by three degrees of freedom, the formulation effectively isolates the nonlinearities of the coordinate transformation. A robust numerical strategy utilizing a modulo function is implemented to resolve the $\pm 2 π$ periodicity singularity, ensuring stable convergence during extreme rigid-body rotations. Internal forces and tangent stiffness matrices are derived via the principle of virtual work, providing a transparent and modular implementation for each beam theory. The accuracy and computational efficiency of the unified formulation are validated through a series of challenging numerical benchmarks involving the geometrically nonlinear analysis of beams, frames, and arches, featuring complex equilibrium paths with limit points and multiple snap-back loops. Comprehensive mesh convergence studies confirm that the shallow arch Euler-Bernoulli element, incorporating explicit axial-bending coupling, achieves superior accuracy and convergence efficiency in problems involving significant geometric nonlinearity.

Study on the Spatiotemporal Evolution Mechanism of Mine Pressure in Gold Mine Mines and its Prediction by FLAC3D Numerical Simulation

Bin Jiang, He Huang, Yalatu Su — Thu, 08 Oct 2026 00:00:00 +0200

Deep underground gold mining induces complex stress redistribution due to high in-situ stress, geological heterogeneity, and progressive excavation, resulting in roof instability, floor heave, and pillar deformation. This study aims to develop a physics-based predictive framework to forecast mine pressure evolution, displacement, and plastic deformation under multiple mining scenarios. The objective is to integrate geological zoning, in-situ stress conditions, and excavation sequences into a unified model to identify high-risk zones and optimize mining strategies. This study utilizes the publicly available FLAC3D Gold Mining Dataset from Kaggle to define mining layout, geometric parameters, in-situ stress, and rock mass properties for the simulation. Spatiotemporal analysis evaluates principal stresses, Von Mises stress, displacements, and plastic zone evolution at each excavation step, revealing areas prone to instability. In addition, the spatiotemporal stress development at baseline, high-stress, deep-mining, and critical scenarios was quantitatively assessed by means of parameters derived from the simulations, allowing for the mapping of high-risk areas and the examination of stress redistribution processes. Finally, the framework predicts stress redistribution and deformation trends under baseline, high-stress, deep-mining, and critical scenarios, validated through numerical comparison with FLAC3D outputs to ensure reliability and accuracy. Results indicate accumulated stress increases from 30 MPa to 750 MPa across mining stages, with prediction errors within ±2MPa,R2=0.97, and RMSE=0.964 MPa. The framework effectively identifies critical stress zones and informs optimal excavation planning, demonstrating its potential to enhance safety and operational efficiency in deep gold mining.

European Journal of Computational Mechanics

A Unified Corotational Framework for 2D Beams: Bridging the Crisfield and Krenk Formulations

Study on the Spatiotemporal Evolution Mechanism of Mine Pressure in Gold Mine Mines and its Prediction by FLAC3D Numerical Simulation