两端固支叠层梁层间接触压力的状态空间解

State Space Solution to the Contact Pressure between Layers of a Laminated Beam Fixed at Both Ends

针对求解两端固支叠层梁在任意横向荷载作用下层间接触压力问题提出了一种状态空间法:引入两个待定纵向位移函数,利用弹性力学、分层模型和矩阵理论,导出了两端固支叠层梁层间接触压力的状态空间解,探讨了高跨比、上下层弹性模量比对层间接触应力的影响.算例结果显示:层间接触压力状态空间解与有限元解十分吻合,且具有快速收敛性和相当高的计算精度;高跨比、上下层材料弹性模量比对层间接触压力峰值和分布特征的影响十分显著.

A state space method to obtain the contact pressure between layers of a laminated beam fixed at both ends that is subjected to an arbitrary transverse loading is put forward.By introducing two undetermined longitudinal displacement functions and applying elastic mechanics,lamination model and matrix theory,the state space solution to the contact pressure between layers of the beam is deduced.The influence from span-to-height ratio and elasticity modulus ratio of upper layer to lower one on the contact pressure between layers is investigated.The results show that the state space solution to the contact pressure between layers is in good line with finite element solution,and has fast convergence and considerably high accuracy.The influence from span-to-height ratio and elasticity modulus ratio of upper layer to lower one on the peak and the distribution characteristics of contact pressure is outstanding.