|
|
| |
| 数据驱动比例边界有限元方法及相关不确定性分析 |
| Data Driven Scale Boundary Finite Element Methodand Relevant Uncertainty Analysis |
| 投稿时间：2025-08-13 修订日期：2025-10-02 |
| DOI： |
| 中文关键词: 比例边界有限元法 应力-应变数据集 数据驱动 不确定性分析 求解规模 |
| 英文关键词:Scale boundary finite element method Stress-strain data set Data driven Uncertainty analysis Solution scale |
| 基金项目:国家自然科学基金(12072063,11972109)资助项目.作者简介杨海天*(1956-),男,博士,博士生导师(E-mail：haitian@dlut.edu.cn). |
|
| 摘要点击次数: 65 |
| 全文下载次数: 0 |
| 中文摘要: |
| 利用比例边界有限元方法（SBFEM）和应变-应力数据集，提出一种无本构求解线弹性问题的数值方法。对均质问题仅需在边界上进行求解，从而有效降低了求解规模；对非均质问题，可利用比例边界有限单元进行全域离散求解。所提方法利用SBFEM的半解析性、便于处理应力奇异性问题及网格剖分问题等的优点，以提高计算精度和计算效率。为考虑数据集不确定性的影响，建立了一个基于区间/随机不确定性模型的应力-应变数据集，并采用粒子群优化方法及蒙特卡洛模拟对位移、应力、应变的区间上下界及均值、方差进行了计算。通过受内压圆环、含裂纹方板拉伸等问题的求解，对所提方法的有效性进行了数值验证，与收敛的比例边界有限元解相比，结果令人满意。同时，探讨了数据集构造、数据集密度、伪弹性参数、比例边界单元数量等因素对计算精度和计算效率的影响。 |
| 英文摘要: |
| Leveraging scale boundary finite element method (SBFEM) and strain-stress data set, a numerical algorithm is presented to solve linear elastic problems in the absence of constitutive parameters. For the homogeneous case,the solution process only needs to conduct on the boundary, such that the solution scale can effectively be reduced. For the heterogeneous case, scale boundary finite elements can be employed in the whole domain solution process. The merits of SBFEM with semi-analyticity and convenience to handle stress singularity and mesh generation, can be utilized to improve computing accuracy and efficiency. On the other hand, an interval/probabilistic uncertainty based strain-stress data set is established, and the intervals, means and variances of strain, stress and displacement are evaluated using the particle swarm optimization algorithm and MCS technique. The effectiveness of proposed algorithm is verified via numerical examples, including an annulus with uniform internal pressure, and a plate with a crack and uniform tension etc. In comparison with the converged SBFEM solutions, satisfactory results are achieved. Meanwhile the impacts of the form and density of strain-stress data set, virtual elastic parameters and the number of SBFE on the computing accuracy and efficiency are investigated. |
| 查看/发表评论 下载PDF阅读器 |
|
|
|
|
