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力学学报  2015 

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, PP. 762-771

Keywords: 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

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Abstract:

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.

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