This paper presents a machine learning-based finite element construction method (MLBFE) to predict a precise strain field with minimal nodes. The method first establishes a standardized MLBFE model via the substructure concept and the static condensation method. Then, a training data collection method involving nodal displacements and strain fields, and considering (1) boundary continuity, (2) strain field continuity, and (3) the effect of rigid body motion, is developed. Furthermore, multivariate linear regression is adopted as the strain field prediction model for the MLBFE. The stiffness matrix and restoring forces of the MLBFE are calculated by employing the principle of virtual work and considering rigid body motion. Compared with common finite element models, the MLBFE enables refined structural simulation with fewer elements and nodes, reducing the number of degrees of freedom and computational costs. Moreover, the MLBFE exhibits high generalizability because it does not rely on specific structures or materials. This paper provides a detailed establishment of MLBFE-based planar elements and investigates the impact of the elemental settings on the computational accuracy of the elastic structural response. The ability of the MLBFE for nonlinear structural analysis is also verified.

中文翻译：

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用于开发基于机器学习的结构分析有限元模型的框架


本文提出了一种基于机器学习的有限元构造方法 （MLBFE），用于预测具有最小节点的精确应变场。该方法首先通过下部结构概念和静态冷凝法建立了标准化的 MLBFE 模型。然后，开发了一种涉及节点位移和应变场的训练数据收集方法，并考虑了 （1） 边界连续性，（2） 应变场连续性和 （3） 刚体运动的影响。此外，采用多元线性回归作为 MLBFE 的应变场预测模型。MLBFE 的刚度矩阵和恢复力是通过采用虚拟功原理并考虑刚体运动来计算的。与常见的有限元模型相比，MLBFE 能够使用更少的单元和节点进行精细的结构仿真，从而减少自由度数量和计算成本。此外，MLBFE 表现出高度的泛化性，因为它不依赖于特定的结构或材料。本文详细介绍了基于 MLBFE 的平面单元，并研究了单元设置对弹性结构响应计算精度的影响。MLBFE 的非线性结构分析能力也得到了验证。