| 梁的轴力非线性静力问题的进一步研究 |
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| 引用本文： | 梁枢平,刘洋,杨永波,郑文衡.梁的轴力非线性静力问题的进一步研究[J].华中科技大学学报(自然科学版),2005,33(2):116-118. |
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| 作者姓名： | 梁枢平 刘洋 杨永波 郑文衡 |
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| 作者单位： | 华中科技大学,土木工程与力学学院,湖北,武汉,430074;华中科技大学,土木工程与力学学院,湖北,武汉,430074;华中科技大学,土木工程与力学学院,湖北,武汉,430074;华中科技大学,土木工程与力学学院,湖北,武汉,430074 |
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| 基金项目： | 国家自然科学基金资助项目(40174024). |
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| 摘 要： | 采用微分求积法(Differential Quadrature Method)和广义微分求积法则(Generalized Differential Quadrature Rule)分析了轴力影响不可忽略时简支梁的非线性静力问题，求出了问题的数值解．列出了两种不同的微分方程，其中GDQR用来求解四阶微分方程，DQ用来解二阶微分方程，并分别采用牛顿-拉弗森法和一般迭代法求解，结果表明这两种方法都比较有效，且各有所长，进一步说明了微分求积法在求解非线性微分方程方面的优势，验证了所得结果的正确性．
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| 关 键 词： | 两端不可动简支梁 微分求积法 广义微分求积法则 轴力 几何非线性 |
| 文章编号： | 1671-4512(2005)02-0116-03 |
| 修稿时间： | 2004年6月21日 |
Improvement of the geometrically nonlinear analysis of immovably simply supported beams by the DQM |
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| LIANG Shuping,Liu Yang,Yang Yongbo,Zheng Wenheng.Improvement of the geometrically nonlinear analysis of immovably simply supported beams by the DQM[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2005,33(2):116-118. |
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| Authors: | LIANG Shuping Liu Yang Yang Yongbo Zheng Wenheng |
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| Institution: | Liang Shuping Liu Yang Yang Yongbo Zheng Wenheng Prof., College of Civil Eng. & Mech.,Huazhong Univ. of Sci. & Tech.,Wuhan 430074,China. |
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| Abstract: | A generalized differential quadrature rule (GDQR) and the differential quadrature method (DQM) were applied to obtain the nonlinear static solution of an immovably simply supported beam. A beam was considered when tensile forces might be neglected. The deflections obtained by two different equations agreed with each other, and they were in agreement with the theoretic solution. The Newton-Raphson method and the general iteration method were applied in GDQR and DQ compution process respectively. GDQR was proposed to solve the fourth-order differential equation, on the other hand, DQ was utilized to solved the second-order differential equation. |
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| Keywords: | immovably simply supported beams DQM GDQR tensile force geometrically nonlinear |
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