| 弹性地基上固支矩形中厚板弯曲问题的辛方法研究 |
| |
| 引用本文： | 杨有贞.弹性地基上固支矩形中厚板弯曲问题的辛方法研究[J].宁夏大学学报(自然科学版),2011,32(4):371-374,379. |
| |
| 作者姓名： | 杨有贞 |
| |
| 作者单位： | 宁夏大学物理电气信息学院,宁夏银川,750021 |
| |
| 基金项目： | 国家自然科学基金资助项目(11047024);宁夏自然科学基金资助项目(NZ1155);宁夏大学自然科学基金资助项目((E)ndzr10-3,ndzr09-39) |
| |
| 摘 要： | 利用Hellinger-Reissner二类变量广义变分原理,推导了弹性地基上中厚板弯曲问题的哈密顿求解体系,采用辛几何方法对全状态相变量进行分离变量,按本征函数展开法得到问题的辛本征通解.由于在求解过程中不需要事先人为选取挠度函数,而是从地基上中厚板弯曲的基本方程出发,直接利用数学方法求解,使得这类问题的求解更加合理...
|
| 关 键 词： | 弹性地基 中厚度矩形板 辛方法 |
Symplectic Solution for the Rectangular Thick Plate on Elastic Foundation with Clamped Edges |
| |
| Yang Youzhen.Symplectic Solution for the Rectangular Thick Plate on Elastic Foundation with Clamped Edges[J].Journal of Ningxia University(Natural Science Edition),2011,32(4):371-374,379. |
| |
| Authors: | Yang Youzhen |
| |
| Institution: | Yang Youzhen(School of Physics and Electrical Information Engineering,Ningxia University,Yinchuan 750021,China) |
| |
| Abstract: | Based on the general variational principle of two variables, Hamiltonian system for moderately thick plate on elastic foundation bending problem was deduced. The corresponding transverse eigenproblem was derived by separation of variables of full state vector by symplectic geometry method. With the solved symplectic eigen-values, the generalized symplectic eigen-solution was given by eigen-funetion expansion. Based on the basic elasticity equations of moderately thick plates, it is not need to prior select the deformation function arbitrary. Therefore, the solution in the paper is reasonable. In order to show the correction of formulations, a numerical examples is presented. |
| |
| Keywords: | elatic foundation moderately thick rectangular plate symplectic geometry method |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
