【作者】 黄亮；

【导师】 刘一华；

【作者基本信息】 合肥工业大学 ， 建筑与土木工程（专业学位）， 2014， 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，对上表面受分布荷载作用的双层叠合悬臂梁进行了理论研究和数值分析，主要内容如下：推导出了均质材料双层叠合悬臂梁上表面分别受均布和线性荷载作用时应力和位移的弹性力学解，对均布荷载作用时，给出了自由端的两种简化形式，并就自由端的两种简化形式和接触面上的摩擦对解的影响进行了讨论。研究结果表明，自由端的第二种简化形式比第一种好；接触面上的摩擦可减小梁中应力，但起到的作用非常小，与光滑界面情况相差不大。推导出了功能梯度材料双层叠合悬臂梁上表面分别受均布和线性荷载作用时应力和位移的弹性力学解，给出了中性层的基本方程。研究结果表明，各层的中性层位置向弹性模量大的一侧偏移。为了检验上述解析解的正确性，运用有限元分析软件ANSYS12.1对分别受均布和线性荷载作用的均质和功能梯度材料叠合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，从而验证了解析解的正确性。更多还原

【Abstract】 Based on the basic equation of plane elasticity, this paper provides both analytical andnumerical researches for two-layered superposed cantilever beams under uniform or linearload on the upper surface by using the Airy stress function method. The study shows asfollows.The elasticity solutions are deduced for the stresses and displacements of two-layeredhomogeneous superposed cantilever beam when subjected to uniform or linear loads on theupper surface. For the beam subjected to uniform load, two kinds of the simplified methodsof free end are introduced and discussed. Moreover, the influence of friction on the contactbetween the two layers has also been included in the discussion. The research shows thatthe second kind of the simplified method is better, and the stress within the beam could bereduced by friction. However, such effect is so limited that it can be ignored and treated assmooth.The elasticity solutions are also deduced for the stresses and displacements oftwo-layered FGM superposed cantilever beam under uniform or linear loads on the uppersurface. A function of the location of neutral surface is introduced. The study shows that thelocation of the neutral surface would shift to the side with larger Young’s Modulus.In order to verify the correctness of the analytical solution in this paper, numerical studywas introduced to calculate different computing models of superposed cantilever beam byusing finite element software ANSYS12.1. The results are in accordance with the analyticalones, which verifies the analytical solution.更多还原