面内变刚度功能梯度圆形薄板的轴对称弯曲

Axisymmetric bending of fuctionally graded thin circular plates with in-plane stiffness gradient

文章提出了面内功能梯度材料圆形薄板受轴对称载荷弯曲变形的理论求解方法,并通过有限元编程计算验证了该理论解的有效性。假定杨氏模量沿半径方向连续梯度变化,而泊松比的变化忽略不计,基于薄板小挠度弯曲理论,分别求解不含孔的圆板和含圆孔的圆板弯曲问题。运用文中的计算方法,将结果退化至普通薄板,能完全吻合经典解;对于给定的一种功能梯度材料参数变化函数,理论解与有限元方法计算结果一致。该文提出的方法在计算效率和精度方面都有一定的优越性,可为未来功能梯度材料在动态分析及主动控制方面的应用提供理论支持。

A theoretical method for solving the bending of fuctionally graded thin circular plates with in-plane stiffness gradient subjected to axisymmetric loads is presented,and then finite element method is used to verify the validity of the previous theoretical solution.The Young’s modulus varies gradually along the direction of radius,and the change of Poisson’s ratio is neglected,the bending of circular plates with or without a circular hole is calculated based on the classic theory of small deflection bending of thin plates.By simplifying the solution to normal plates,its result coincides with the classic results.Given the parameter function of fuctionally graded material,the theoretical solution can also coincide with the finite element results.Computational methods presented in this paper have superiorities in efficiency and accuracy in order to provide proof for the next step of dynamic analysis and active control.