具有梯度界面层的双材料悬臂梁解析解

Analytical solution for bi-material cantilever beam with graded interface layer

采用应力函数法,求得了具有弹性模量沿高度线性变化的梯度界面层的双材料悬臂梁在均布载荷作用下的应力和位移解析解。该解可退化为双材料梁、弹性模量沿整个梁高线性变化的梯度梁以及均质材料梁的情况,退化为均质材料梁时与已有结果一致。通过一具体算例将得到的解析解与有限元解进行了比较,两者吻合较好。并讨论了梯度界面层的高度变化对梁中的应力和梁端挠度的影响。结果表明,在梁的总高度不变的情况下,增加梯度界面层的高度可减小弯曲应力和梁端挠度,而对挤压应力和切应力的影响很小。

Using the airy stress function method,an analytical solution is obtained for a bi-material cantilever beam with a graded interface layer,in which Young's modulus varies linearly through its height and Poisson's ratio is constant,subjected to uniform load.The solution can degenerate into the case of the bi-material beam or the graded one in which Young's modulus varies linearly through the whole height.It can also degenerate into the solution of the homogeneous beam which can be found in the literature.An example is analyzed,and the analytical results obtained in this paper coincide with the numerical ones obtained by the finite element method.Finally,the change of the stresses and deflection of the end of the beam versus the height of the graded interface layer is discussed.It is found that the bending stress and deflection decrease when the height of the graded interface layer increase,but the bearing and shearing stresses are nearly not influenced.