| 高可乐， 王克用， 李培超.考虑体力的轴对称弹性问题杂交基本解有限元法[J].轻工机械,2020,38(1):5-11 |
| 考虑体力的轴对称弹性问题杂交基本解有限元法 |
| Hybrid Fundamental Solution Finite Element Method for Axisymmetric Elasticity with Body Force |
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| DOI：10.3969/j.issn.1005 2895.2020.01.002 |
| 中文关键词: 轴对称弹性问题 体力 基本解有限元法 特解 |
| 英文关键词:axisymmetric elasticity body force fundamental solution finite element method particular solution |
| 基金项目:上海市自然科学基金项目（19ZR1421400）。 |
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| 摘要点击次数: 783 |
| 全文下载次数: 933 |
| 中文摘要: |
| 针对含体力轴对称弹性问题中精确解求解困难、传统有限元网格畸变免疫性差以及复杂问题网格密度大等问题，课题组提出了一种杂交Trefftz基本解有限元计算格式。在数值求解过程中，体力项的存在，会导致单元刚度方程涉及域积分，从而使杂交基本解有限元法只含边界积分的优势消失且计算效率降低。为保持该有限元法的优势和计算效率，可将问题的全解分为齐次解和特解2部分求解，来达到消除域积分的目的。[JP2]对不同计算方法下得到结果进行对比，表明该方法准确、高效，对网格畸变有良好的免疫性。该有限元模型能更好地适用于对含体力轴对称弹性问题的数值求解。 |
| 英文摘要: |
| Aiming at solving the difficulty of the exact solution, the poor mesh distortion immunity and the high grid density about complex problems of conventional finite element method in the axisymmetric elasticity problems with body force, a hybrid Trefftz fundamental solution finite element method was proposed to obtain the solution. In this process, the existence of the body force leads to the element stiffness equation involving domain integration, so that the boundary only formulation advantage of the hybrid fundamental solution finite element method is eliminated and the computational efficiency is reduced. In order to maintain the advantages and computational efficiency of this finite element method, the complete solution of the problem can be divided into a two part solution of the homogeneous solution and the particular solution to eliminate the domain integral. By comparing the results obtained by different calculation methods, it is indicated that the method has accuracy, higher efficiency and good mesh distortion immunity. The finite element model can be used to solve the problems of axisymmetric elasticity with body force. |
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