双材料层合梁弯曲正应力的弹性解与试验分析

Flexible Solution and Experimental Analysis on Bending Normal Stress in Bi-material Laminated Beam

利用双材料层合梁弯曲时的轴向静力平衡方程,确定了双材料层合梁弯曲时中性层的位置,采用弹性力学方法推导出了双材料层合梁拉伸区及压缩区弯曲正应力的表达式。通过层合梁的弯曲应力试验,验证了弹性力学方法给出的双材料层合梁弯曲正应力计算公式的正确性。通过试验及理论计算可知:弹性力学方法计算结果、材料力学方法计算结果与试验结果基本吻合;弹性力学方法给出的层合梁弯曲正应力公式考虑了剪切变形对层合梁弯曲正应力的影响,所以弹性力学方法对测试点的计算结果大部分优于材料力学方法对测试点的计算结果。讨论分析表明,弹性力学方法推导出的双材料层合梁弯曲正应力公式计算结果与试验结果较为接近,可以在实际工程中推广应用。

Using the axial static equilibrium equation,the location of the neutral layer of the bending bi-material laminated beam is determined.Based on the elastic mechanics method,the calculation formulas of the bending normal stress on the stretching zone and the compression zone in the bi-material laminated beam are obtained.After the bending stress experiment on the laminated beam,it is verified that the calculation formula of the bending normal stress in the bi-material laminated beam by the elastic mechanics method is correct.The experiment and theoretical calculation show that the calculation results by the elastic mechanics and the material mechanics are basically consistent with the experimental results.Because the elastic mechanics takes into account the influence of the shear deformation on the bending normal stress of the laminated beam,the calculation results on the test points are better than most of the material mechanics.The analysis shows that the calculation results of the bending normal stress in the bi-material laminated beam by the elastic mechanics method are closer to the experimental values,so this method can be extended in practical engineering.