SEAT2D-GNN: A Seat-Inspired Elastodynamics Database with Geometric and Topological Variations on 2D Meshes, e.g. for Graph Neural Network Applications

Overview This database contains results from linear elastodynamic simulations performed on 2D “seat” geometries. The dataset comprises 1,800 examples generated using random configurations of holes (round or square), with six different parameterizations (1 round hole, 2 round holes, 3 round holes, 1 square hole, 2 square holes, 3 square holes). The geometries are grouped by sets of six in ascending order of their index. All simulations were carried out with linear T3 finite elements and time integration was done using the Newmark scheme. Matlab Files: seat_lin_i.mat Each seat_lin_i.mat file contains the following data: M: Mass matrix K: Stiffness matrix F: Time-dependent loading term ddlu: Boolean indices indicating free degrees of freedom lt: List of 400 time steps Uref: Primal solution field (displacements) over time The equation solved in these simulations is: M d2Uref/dt2 + K Uref = F. Python Reader: transfer_mat2py.py A Python script, transfer_mat2py.py, is provided to facilitate reading the .mat files within a Python environment. This script allows users to import the simulation data (mass matrix, stiffness matrix, loading terms, etc.) directly into their Python workflows. Python Files: seat_i.pt Each seat_i.pt file is stored in the torch_geometric.data “graph” format and contains: Node features: X: Node positions and local contributions of the stiffness matrix N: Node type (Dirichlet, non-zero Neumann, or zero Neumann) F: Loading term at each node Edge features: edge_attr: Stiffness matrix contributions associated with each edge edge_index: Graph connectivity Output fields: s1: First spatial mode of the primal solution s2: Second spatial mode of the primal solution s3: Third spatial mode of the primal solution This dataset can be used to develop and benchmark methods for reduced-order modeling, machine learning approaches in computational mechanics, or any application that requires detailed finite element simulations of linear elastodynamics on heterogeneous 2D geometries.

概述 本数据库收录了针对二维“座椅”几何结构开展的线性弹性动力学模拟结果。本数据集包含1800个样本，均通过随机配置的圆孔或方孔生成，涵盖6种不同参数设置：1个圆孔、2个圆孔、3个圆孔、1个方孔、2个方孔、3个方孔。所有几何结构按索引升序每6个分为一组。所有模拟均采用线性T3有限元（linear T3 finite elements）进行，时间积分使用纽马克（Newmark）格式完成。
Matlab文件：seat_lin_i.mat
每个seat_lin_i.mat文件包含以下数据：M：质量矩阵（Mass matrix），K：刚度矩阵（Stiffness matrix），F：时变载荷项，ddlu：指示自由自由度的布尔索引，lt：包含400个时间步长的列表，Uref：随时间变化的本原解场（位移场）。本模拟求解的方程为：$M frac{mathrm{d}^2 U_{ ext{ref}}}{mathrm{d}t^2} + K U_{ ext{ref}} = F$。
Python读取工具：transfer_mat2py.py
提供Python脚本transfer_mat2py.py，用于在Python环境中读取.mat格式文件。该脚本可帮助用户直接将模拟数据（质量矩阵、刚度矩阵、载荷项等）导入Python工作流。
Python文件：seat_i.pt
每个seat_i.pt文件以PyTorch几何（torch_geometric.data）的“图”格式存储，包含以下内容：
节点特征：X：节点位置与刚度矩阵的局部贡献，N：节点类型（狄利克雷（Dirichlet）、非零诺依曼（Neumann）或零诺依曼），F：每个节点的载荷项。
边特征：edge_attr：与每条边相关联的刚度矩阵贡献，edge_index：图连通性。
输出场：s1：本原解的第一空间模态，s2：本原解的第二空间模态，s3：本原解的第三空间模态。
本数据集可用于开发和基准测试降阶建模、计算力学中的机器学习方法，以及所有需要对非均匀二维几何结构开展线性弹性动力学精细有限元模拟的相关应用。