任意厚度梁的动力与稳定解析解（英文）

Exact Analytical Solution for Laminated Beams with Arbitrary Height

通常对于静力、动力与稳定问题的叠层梁仅能得到近似解。本文基于弹性力学的基本方程和状态空间理论,抛弃任何有关应力和位移模式的假定,导出梁的状态方程,得出状态方程变量级数表达式。采用Cayley-Hamilton定理,有效处理静力、动力和稳定问题,得出在任意荷载作用下任意高度叠层梁的封闭解析解。算例结果与有限元解对比,计算高效精确。

The approximate solution usually can only be obtained on solving the problem of statics, dynamics and buckling of laminated beams with arbitrary height. Based on the theory of elasticity and the method of state space, the state equation for isotropic laminated beam with simply supported edges is established without any assumptions about displacement models and stress distributions. Series expansion was carried out on the variables of the state equation. Using Caley-Hamilton theory, the exact closed analytical solutions are presented for statics, dynamics and buckling of laminated beams with arbitrary height. The method of calculating critical loads is improved in present. Numerical results of the example are obtained and compared with finite element method. The results show that the convergent solution can be achieved with high accuracy.