预应力CFRP加固简支梁的弹性力学解析解

ELASTICITY ANALYTICAL SOLUTION OF SIMPLY SUPPORTED BEAMS STRENGTHENED WITH PRESTRESSED CFRP SHEET

以预应力CFRP加固简支梁为例,研究梁上表面受荷载作用时CFRP预应力和层数对简支梁应力和位移分布的影响。首先,将简支梁和CFRP沿界面切开各自进行分析,基于二维弹性力学理论,对简支梁进行分析;利用受张力的弦变形理论,对预应力CFRP层进行分析。然后,根据梁和CFRP层间的界面应力和位移连续条件以及梁上表面的载荷条件确定待定系数,最终得到CFRP加固简支梁的应力和位移精确解析解。数值结果与有限元软件ANSYS分析高度一致。研究表明CFRP的预应力和层数对简支梁的应力和位移分布均有影响,预应力越大、层数越多,梁的正应力和竖向位移越小。

Taking the simply supported beam strengthened with prestressed CFRP as an example,the effect of prestress value and layer number of CFRP on the stress and displacement distributions of the beam under static loads is studied. Firstly,the beams and CFRP sheets are considered separately. The beam is studied based on the two-dimensional elasticity. The CFRP sheet is analyzed by the string theory. Then,the unknown constants in expressions of displacements and stresses are obtained by the continuity of displacements and stresses between the beam and the CFRP sheet. Finally,the exact analytical solution of displacements and stresses in the beam are obtained. Comparing the results with those obtained from ANSYS shows the high precision of the present method. The results show that the prestressing sheet and the layer number of CFRP have important effects on the beam. The greater the prestressing force of CFRP and the more number of CFRP layers,the smaller stresses and displacements of the beam are.