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| 一类非线性发展方程组的隐式解析解 | |
| 引用本文： | 王然,袁学刚,张洪武,吕娜.一类非线性发展方程组的隐式解析解[J].大连民族学院学报,2016,18(3):230-232. |
| 作者姓名： | 王然 袁学刚 张洪武 吕娜 |
| 作者单位： | 1.大连理工大学 结构分析和工业装备重点实验室,辽宁 大连116024; 2.大连民族大学 理学院,辽宁 大连 116605 |
| 基金项目： | 辽宁省教育厅高校优秀人才支持计划(LR2012044);中央高校基本科研业务费专项资金资助项目(DC201502050203,DC201502050403)。 |
| 摘 要： | 研究了一类非线性发展方程组的求解问题。该方程组可用于描述由各向同性近似可压缩neo-Hookean材料组成的圆柱管在轴向载荷作用下的轴对称运动。首先通过变分原理导出了描述圆柱管径向和轴向对称运动的非线性发展方程组;然后利用行波变换将其约化为非线性常微分方程组;最后得到首次积分,进而给出了此类非线性发展方程组的隐式解析解。 |
| 关 键 词： | 非线性发展方程组 超弹性圆柱管 非线性运动 隐式解析解 |
Implicit Analytical Solutions for a System of Nonlinear Evolution Equations |
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| WANG Ran,YUAN Xue-gang,ZHANG Hong-wu,LV Na.Implicit Analytical Solutions for a System of Nonlinear Evolution Equations[J].Journal of Dalian Nationalities University,2016,18(3):230-232. | |
| Authors: | WANG Ran YUAN Xue-gang ZHANG Hong-wu LV Na |
| Institution: | 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian Liaoning 116024, China ; 2.School of Science, Dalian Minzu University, Dalian Liaoning 116605, China |
| Abstract: | This paper investigates the problem for solving a system of nonlinear evolution equations. The system can be used to describe the axisymmetric motion of a cylindrical tube composed of a class of isotropic approximate compressible neo-Hookean material models. Firstly, the system describing the radially symmetric and axisymmetric motion of the cylindrical tube is derived by the variational principle. Then the system can be reduced to a system of nonlinear ordinary differential equations by the traveling wave transformation. Finally, the first integral is obtained, and the implicit analytical solutions of the system of nonlinear evolution equations are given. |
| Keywords: | system of nonlinear evolution equations hyperelastic cylindrical tube nonlinear motion implicit analytical solution |
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