含固支边矩形叠层厚板的状态空间新解法

胡文锋; 刘一华

doi:10.6052/0459-1879-15-033

含固支边矩形叠层厚板的状态空间新解法

doi: 10.6052/0459-1879-15-033

胡文锋,
刘一华^,

合肥工业大学土木与水利工程学院, 合肥230009

详细信息

通讯作者:
刘一华,教授,主要研究方向:弹性力学,复合材料力学.E-mail:liuyihua@hfut.edu.cn

中图分类号: O343.8
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出版历程
- 收稿日期: 2015-01-22
- 修回日期: 2015-06-15
- 刊出日期: 2015-09-18

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

Hu Wenfeng,
Liu Yihua^,

School of Civil Engineering, Hefei University of Technology, Hefei 230009, China

摘要

摘要: 通过把固支边上的边界位移函数作为状态变量引入状态方程,得到了含固支边矩形单层与叠层厚板的精确解. 在求解过程中,将非齐次状态方程的求解变为齐次状态方程的求解,省略了求解待定常数的中间过程,使求解过程变得简单. 所得到的解能够严格满足固支边界条件,在同一材料层内不需作分层处理,因而更加精确. 此外,对固支边的应力提出了新的计算方法,能够得到更精确的边界应力. 算例表明,本文解比现有精确解收敛快,与有限元解吻合的更好,尤其是在固支边处体现得更加明显.
- 矩形叠层厚板 /
- 固支边 /
- 边界位移函数 /
- 状态变量 /
- 状态方程 /
- 精确解
Abstract: Based on the Refs.[1-3], boundary displacement functions are treated as state variables and introduced into the state equation. The exact solutions are presented for the rectangular thick single and laminated plates with clamped edges. In the solving process, the state equation becomes a homogeneous equation from a nonhomogeneous one and the intermediate process to solve undetermined constants is omitted. The displacement boundary conditions are satisfied strictly on clamped edges, and it is not necessary to divide the layer with same material into some sub-layers. Therefore the obtained solutions are more accurate. Additionally, a new calculating method of the stresses on the clamped edges is proposed and more exact boundary stresses can be obtained. The results of two examples show that the present solutions have better constringency and higher precision, and are approaching to FEM solutions well than the existing exact solutions, especially on the clamped edges.
- rectangular thick laminate /
- clamped boundary /
- boundary displacement function /
- state variable /
- state equation /
- exact solution

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参考文献(23)

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