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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。
Generally, only the approximate solution can be obtained for the laminated beam with static, dynamic and stability problems. Based on the basic equations of elasticity and the theory of state space, this paper discards any assumptions about stress and displacement modes and derives the equation of state of the beam to obtain the expression of the order of magnitude of the state equation. The Cayley-Hamilton theorem is used to deal with the static, dynamic and steady-state problems effectively. The closed analytical solution of any height-piled beam under any load is obtained. The result of the example is compared with the finite element solution, and the calculation is efficient and accurate.