| 郑子君,王洪.模拟滚弯非稳态过程的虚拟载荷法[J].计算力学学报,2021,38(1):8~14 |
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| 模拟滚弯非稳态过程的虚拟载荷法 |
| An artificial load method to simulate non-steady state of roll bending |
| 投稿时间：2020-03-06 修订日期：2020-07-09 |
| DOI：10.7511/jslx20200306002 |
| 中文关键词: 滚弯 欧拉网格 虚拟载荷 弹塑性分析 有限元法 |
| 英文关键词:roll bending Eulerian grid artificial load elastoplastic analysis finite element method |
| 基金项目:国家自然科学基金青年项目（11702046）；重庆市教委科学研究项目（KJ1600910）资助项目. |
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| 中文摘要: |
| 采用传统的拉格朗日有限元模型模拟三辊滚弯的非稳态过程时，受到网格数量和接触算法的影响，计算效率难以提高。受计算流体力学的启发，将滚弯机跨内空间视作一维流场，工件挠曲线视作流场中的变量，采用欧拉观点建模，可以大大减小网格数量，同时降低接触处理的难度。将欧拉观点控制方程中的迁移项归结成一个附加的虚拟载荷，将其定义为型材空间构型不变而材料流动导致的内力不平衡量。通过引入该载荷，在经典平面梁单元的基础上稍加修改，得到适于小曲率滚弯模拟的欧拉单元平衡方程。算例表明，在相同网格尺寸下，虚拟载荷法和传统的有限元模拟结果均与理论解吻合良好；但前者的计算效率更高，结果更加光滑可靠。 |
| 英文摘要: |
| The conventional simulation of the non-steady-state of the structural steel roll bending suffers from the mesh scale and the contact algorithm employed,and thus is not very efficient.Inspired by computational fluid dynamics,the space between the bottom rollers is taken as a one-dimensional flow field,while the deflection of the work-piece as the field variable.Thus an Eulerian mesh with a much smaller grid number is employed,which significantly simplifies the contact treatment as well.The convective term in the Eulerian governing equation is considered as an artificial load,whose definition is the internal force unbalance when the material flows in the tangential direction but the configuration remains unchanged.By introducing the concept of an artificial load,the finite element formula is established by slightly modifying the classic Hermite planar beam element equation.The numerical example shows that by using the same element size,the proposed method and the conventional plane stress simulation scheme both delivers results close to the analytic solution.However,the proposed method is more efficient,and its result is smoother and more credible than the conventional simulation schemes. |
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