简支叠层梁的线弹性精确解

The Liner Elastic Accurated Solution for Simple Support Laminated BeamI

本文抛弃了梁的简化理论中有关位移或应力模式中的任何人为假设，也不采用弹性力学经典解对梁端边界所做的简化，而是从梁的平面弹性理论模型出发，通过把Ｆｏｕｒｉｅｒ级数与状态空间法以及传递矩阵技术相结合，给出了两端简支叠层梁精确满足所有基本方程和边界条件的弹性理论解，本文的解法属位移与部分应力耦联的混合解法，对梁的长、高比没有任何限制，文中给出的若干算例，旨在从定量的角度说明简支叠层梁已有解答的适用范围。

All assumptions concerning displacement and stress model in beam simplifying theory have been discarded and there is no simplification to boundary couditions as used in elastic me- chanics for ciassical solution in the paper.Based on the plane elastic theroy model of beam,with the combination of Fourier series and state space method and transfer matrix tech- nology,an elastic theoretical solution has been worked out for all fundamental equations and boundary couditious under condition of two ends simple support laminated beam.The method used in the paper is a displacement and partial stress coupled mixing solution. There is no limi- tation on the ratio of length to height.Some examplec have been given to illustrate quantitatively the scope of the solution for simple support laminated beam.