| 钱若军,袁行飞.基于mbS模式的有限单元法[J].计算力学学报,2023,40(3):447~455 |
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| 基于mbS模式的有限单元法 |
| Finite element method based on the MbS model |
| 投稿时间：2021-08-09 修订日期：2021-10-29 |
| DOI：10.7511/jslx20210809001 |
| 中文关键词: mbS模式 有限单元法 扩展形函数 弹塑性力学 能量泛函变分原理 |
| 英文关键词:mbS model finite element method extended shape function elastic-plastic mechanics energy functional variational principle |
| 基金项目:国家自然科学基金（51878600；52278224）资助项目. |
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| 中文摘要: |
| mbS模式及其有限元法是在固体和结构分析模型中引入薄膜、弯曲和剪切理论，且采用纯拉压、纯弯和纯剪单元进行分析的数值方法。在时空系中剖分物质单元和时间单元上构造以指数函数和贝塞尔函数为插入函数且按Lagrange插值条件的薄膜、弯曲和剪切等基本位移函数，由此得到更加完备和耦合的固体和结构实体单元的变形模式，根据能量泛函变分原理得到静动力有限元基本方程的一致格式。研究表明，mbS模式及其有限元法可用于梁柱和板壳等结构的静动力分析及屈曲分析。 |
| 英文摘要: |
| The finite element method based on the MbS model is a numerical analysis method that introduces of membrane, bending and shear theories into solid and structural analysis models, and the adoption of pure tension and compression, pure bending and pure shear elements.The exponential function and Bessel function are constructed as the insertion function on the material unit and time unit divided in the space-time system, and the basic displacement functions such as membrane, bending and shearing are obtained according to Lagrange interpolation conditions.Thus more complete and coupled deformation modes of structural solid units are obtained as well as the consistent format of the basic equations of static and dynamic finite elements according to the variational principle of energy functional.The analysis shows that mbS model and its finite element method can be used in static and dynamic analysis and buckling analysis of beams, columns, plates and shells. |
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