【作者】 朱立军；

【导师】 刘一华；

【作者基本信息】 合肥工业大学 ， 固体力学， 2009， 硕士

【摘要】 本文基于平面弹性力学的基本方程,采用应力函数法,推导出了双材料叠合悬臂梁在自由端受集中力作用时的解析解,该解析解可退化为已有的单材料悬臂梁在自由端受集中力作用时的解析解。研究结果表明:上、下层中的弯曲正应力沿高度分别按线性规律变化;挤压应力为零;切应力沿高度分别按抛物线规律变化;变形后上、下层中的横截面不再保持为平面;叠合梁上、下层中的剪力和弯矩是按刚度分配的,当上层自由端面所受外力之和大于或等于一定数值时,上、下层之间才能保持接触状态。为了检验所得到的解析解的正确性,本文运用有限元分析软件ANSYS10.0对不同叠合形式的悬臂梁进行了数值分析,并将所得到的数值结果与解析解进行了比较,两者吻合较好,从而验证了该解析解的正确性。此外,借助他人的实验结果,对理论分析结果进行了检验,进一步证明了理论分析结果的正确性。更多还原

【Abstract】 Based on the basic equation of the plane elasticity problem, the analytical solution is presented for a bi-material superposed cantilever beam subjected to a concentrated force at the free end by using the stress function method. The solution of the stresses can be degenerated into the one of the single material cantilever beam subjected to a concentrated force at the free end, which can be found in the literatures. The study shows that the bending normal stresses in each layer of the bi-material superposed cantilever beam vary linearly along the height of the layer, the compressive stresses are zero, the shear stresses vary parabolically along the height of the layer. After deformation, the cross sections are not planes again, the shear force and bending moment in each layer of the beam are distributed based on stiffness ratio, and the external force acted at the free end of the upper layer must be not less than a certain value to maintain the contact between the upper layer and the lower one.In order to verify the correctness of the analytical solution obtained in this paper, different computing models of the superposed cantilever beam are calculated numerically by using the finite element software ANSYS10.0. The numerical results coincide with the analytic ones well, which verifies the correctness of the analytical solution. A further proof of the correctness of analytical solution is obtained by comparing others’experimental results with the analytic ones.更多还原