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针对粘结型组合梁,在粘结层仅沿轴向剪切变形的假定下,给出了组合梁大挠度弯曲的一般非线性控制方程,指出仅在一阶近似下,组合梁子梁的轴线挠度相等。其次,在Euler-Bernoulli梁变形的条件下,通过线性化方法,由上述非线性控制方程得到以挠度和轴向位移为基本未知量的组合梁线性弯曲耦合控制方程,该耦合方程组可分别退化为经典组合梁和叠梁的控制方程。最后,分析了悬臂组合梁在端部集中力作用下的线性弯曲,得到了问题的解析解,给出了不同梁长下组合梁自由端挠度、粘结层滑移位移和剪切应力等随粘结层剪切模量和厚度的变化曲线,进行了参数分析,结果表明:粘结层厚度和剪切模量对组合梁挠度和粘结层滑移有较为显著的影响,而对粘结层剪力影响很小。
Aiming at the bond-type composite beam, the general nonlinear governing equations of large deflection bending of the composite beam are given under the assumption that the bonding layer is only axially sheared. It is pointed out that in the first-order approximation, the axis of the composite beam sub- Deflection equal. Secondly, under the condition of the deformation of the Euler-Bernoulli beam, the linear bending governing equations of the composite beam with the deflection and the axial displacement as the basic unknowns are obtained by the linearization method from the above nonlinear governing equations. The coupled equations can be degenerated The governing equations for the classical composite beams and girders. Finally, the linear bending of the cantilever beam is analyzed, and the analytical solution of the problem is given. The deflection of the free end of the composite beam with different beam length, the slip displacement of the bonding layer and the shear stress are given with the bond The results show that the thickness and shear modulus of the bonding layer have a significant influence on the deflection of the composite beam and the slip of the bonding layer, Force impact is small.