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| 三维弹塑性固体大变形分析的无额外自由度广义有限元法 |
| A Generalized Finite Element Method without extra degrees of freedom for large deformation analysis of three-dimensional elastoplastic solids |
| 投稿时间：2024-01-14 修订日期：2024-02-29 |
| DOI： |
| 中文关键词: 广义有限元 额外自由度 非线性分析 弹塑性 大变形 |
| 英文关键词:Generalized Finite Element Method extra degrees of freedom nonlinear analysis elastoplasticity large deformation |
| 基金项目:国家自然科学基金面上项目（12372194），中央高校基本科研业务费（DUT21GF304）资助项目. |
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| 中文摘要: |
| 无额外自由度广义有限元法在保留标准广义有限元法高阶插值特性的同时,还消除了额外自由度引发的求解规模扩大及线性依赖问题。这使得它在弹性分析中,相比于传统有限元表现出了计算精度高、收敛性好的优势,同时在平面问题的非线性分析中也展现出了良好潜力。将该方法推广和应用至三维弹塑性固体的大变形分析,一方面可以进一步探究其在非线性分析中的表现,另一方面则拓展了广义有限元法在非线性问题领域的应用。在非线性弹性和弹塑性两种材料的大变形分析中,将该方法同传统有限元和商软进行了对比,计算结果表明了该方法在精度方面的优势。 |
| 英文摘要: |
| The generalized finite element method (GFEM) without extra degrees of freedom eliminates the issues of the increased scale of a linear system and linear dependence, while preserving the standard high-order interpolation characteristics. This results in advantages such as high computational accuracy and good convergence compared to traditional finite element methods in elastic analysis. Simultaneously, it demonstrates promising potential in the nonlinear analysis of planar problems. The extension and application of this method to large deformation analysis of three-dimensional elastoplastic solids allow for further exploration of its performance in nonlinear analysis and broaden the application of GFEM in the field of nonlinear problems. In the large deformation analysis of nonlinear elastic and elastoplastic materials, this method is compared with traditional finite element methods and commercial software. The computational results demonstrate the superiority of this method in terms of accuracy. |
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