| 卞正宁,杜世森,罗建辉.弹性力学问题的一阶有限元解法[J].计算力学学报,2015,32(4):544~547 |
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| 弹性力学问题的一阶有限元解法 |
| First-order finite element method for elasticity |
| 投稿时间：2014-05-23 修订日期：2014-11-03 |
| DOI：10.7511/jslx201504016 |
| 中文关键词: 有限元 弱形式 弹性力学 一阶解法 应力精度 |
| 英文关键词:finite element weak form elasticity first-order algorithm stress accuracy |
| 基金项目:国家自然科学基金(51278182)资助项目. |
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| 摘要点击次数: 1831 |
| 全文下载次数: 1817 |
| 中文摘要: |
| 求解弹性力学问题的应力时,如果采用常规的位移有限元法,需要先求得单元的节点位移,再经过求导运算得到.为了解决这种求解方式引起的应力精度下降的问题,提出了弹性力学问题的一阶多变量形式,使得应力与位移精度同阶,并推导了弱形式.采用有限元方法,对弹性力学问题给出了一阶解法的二维、三维数值算例,并且将一阶解法的结果与常规位移有限元法的解进行了比较.数值计算结果表明,一阶解法有效提高了应力的精度,并且应力的误差和节点位移的误差具有相同的收敛阶,验证了本文方法的有效性,为提高有限元法的应力精度提供了新的思路. |
| 英文摘要: |
| In the conventional displacement finite element methods,the stresses are obtained from a diffe-rential operation after the nodal displacements are determined,which is not accurate.In order to improve the stress accuracy,a first-order multi-variable form is proposed to make sure the order of stresses and displacements are equal,and the weak form is then derived.Using the finite element method,a two-dimensional and a three-dimensional elastic problem is solved by first-order method respectively,and the first-order solutions and the solutions of the conventional displacement finite element method were compared.The numerical results show that the first-order solution effectively improves the accuracy of the stresses while the displacement errors and the stress errors have the same convergence order,which verify the effectiveness of the method and provides a new idea of improving the stress accuracy of the finite element method. |
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