一种隐式稳定节点光滑有限元分解ALE法及其在大变形分析中的应用 English Version
A decoupled ALE method of implicit stabilized node-based smoothed finite element and its applications to large deformation analysis
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摘要: 岩土工程常涉及土体大变形问题，采用基于小变形假设的有限元法对其进行分析会产生较大计算误差或因网格畸变而导致计算中断。分解任意拉格朗日-欧拉（ALE）法将网格变形与材料变形分离，分别执行更新拉格朗日（UL）步与欧拉步以便克服网格畸变引起的计算精度降低或计算终止问题。将稳定节点光滑有限元（NsFEMstab）法与ALE法相结合，提出一种新的NsFEMstab-ALE法，并提出一种用于网格自适应调整策略的动态布点法。以刚性基础地基大变形问题为例，对NsFEMstab-ALE进行检验，数值结果表明：（1）基于网格自适应调整策略的动态布点法能够有效解决大变形引起的网格畸变问题，实现网格疏密平滑过渡，确保大变形模拟过程中整个网格单元具有良好质量；（2）应用NsFEMstab-ALE法时，能够获得与参考文献相符荷载-位移响应曲线以及合理的等效塑性应变云图和网格变形图。
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关键词:
- 土体大变形 /
- 稳定节点光滑有限元法 /
- 隐式有限元框架 /
- 自适应网格重划分 /
- 任意拉格朗日-欧拉法
Abstract: Large deformation of soil mass has been often encountered in geotechnical analysis. When the small deformation assumption-based finite element method is applied to such large deformation analysis, the computational errors can be accumulated or the computational process may be terminated due to mesh distortion. In the decoupled arbitrary Lagrangian-Euler (ALE) method with separated mesh deformation and material deformation, the updated Lagrangian (UL) step is implemented followed by the Euler step to overcome the reduced computational accuracy or the computational termination caused by mesh distortion. By combining the stabilized node-based smoothed finite element method (NsFEMstab) with the ALE method, a novel NsFEMstab-ALE method is proposed, and furthermore a dynamic placement approach of nodes for the adaptive remeshing strategy is developed. Based on a rigid footing resting on ground involving large deformation, the method of NsFEMstab-ALE is examined, and numerical results show that: (1) by applying the dynamic placement method of nodes, the mesh distortion caused by large deformation can be effectively resolved, the smooth mesh transition from fine-mesh area to coarse-mesh area can be realized, and the good element quality in the whole mesh during the entire deformation process can be guaranteed. (2) the load-displacement curves predicted by the NsFEMstab-ALE method agree well with those in the literatures, and the equivalent plastic strain contours and deformed meshes calculated by the NsFEMstab-ALE method are rational. -
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