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 引用本文: 胡文锋, 刘一华. 含固支边矩形叠层厚板的状态空间新解法[J]. 力学学报, 2015, 47(5): 762-771.
Hu Wenfeng, Liu Yihua. A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 762-771.
 Citation: Hu Wenfeng, Liu Yihua. A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 762-771.

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

• 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.

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.

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