| dc.description.abstract | The Finite Element Method (FEM) has long been widely applied and validated in the analysis of solid mechanics problems. However, when faced with large deformation problems such as explosions, high-speed impacts, complex geometries, and dynamic crack propagation, FEM often encounters challenges such as model construction difficulties and the need for remeshing. In recent years, the Material Point Method (MPM) has become a popular numerical method for addressing these issues due to its ease of model construction and its ability to handle large deformation and motion problems.
This thesis primarily utilizes the Generalized Interpolation Material Point Method (GIMP) to explore the applicability and reliability of MPM in two types of problems: extreme conditions and structural stability. Extreme condition problems include explosions and high-speed impacts, which involve severe large deformations and high strain rates. Due to GIMP′s capability to effectively handle these complex phenomena, it demonstrates unique advantages under such extreme conditions. Additionally, structural instability problems, such as buckling induced by slight eccentricity, also pose a significant challenge for simulation.
In terms of research methods, this study conducts convergence analysis with different speeds and mesh divisions for high strain rate problems under extreme conditions. For structural stability problems, the buckling of columns is numerically simulated to investigate the impact of different eccentricities on the load response of specimens, and the accuracy of three stress extraction methods is compared.
The results show that under high strain rate conditions, ensuring the deformation speed is lower than the material′s stress wave velocity allows MPM to accurately simulate the material′s stress-strain behavior. As the mesh refinement increases, the simulation results become closer to theoretical solutions, although computational complexity and time costs also increase. Furthermore, the study indicates that under different eccentricities, the reaction force curves at the fixed ends of the specimens closely match theoretical solutions, confirming the reliability of MPM in analyzing structural buckling phenomena.
This research confirms the application potential of MPM in high strain rate and stability problems and provides reference suggestions for future numerical simulations, contributing to improving the accuracy and reliability of engineering design and analysis. | en_US |