微分求积法求解变截面功能梯度梁的弯曲问题

Bending of Functionally Graded Beam with Variable Cross-Sections by Differential Quadrature Method

应用微分求积法(DQM)分析变截面功能梯度梁的弯曲.基于Euler梁理论,同时考虑横截面尺寸和材料参数沿长度梯度变化,建立基本方程.采用DQM对变系数高阶微分方程进行数值求解.首先,退化为等截面均匀材料梁得到数值结果,并与解析解比较,说明了DQM的有效性和精确性.其次,分别考虑横截面尺寸和材料物性参数沿轴向连续变化,给出功能梯度梁的挠度的数值解,并分析几何参数、物理参数沿轴线变化时梁挠度的变化规律.

The bending of functionally graded material （FGM） beam with variable cross-sections is ana- lyzed by using differential quadrature method （DQM）. Based on the theory of Euler beam,considering the variations of cross-section and gradient of the materials along the axial coordinate,the governing equations are derived. DQM is used to numerically solve higher order differential equations with variable coefficients. Firstly, comparisons between the numerical results and analytical results for the homogenous beam are giv- en, which shows the efficiency and accuracy of the DQM. Then, deflections of the FGM beam with the varied material properties and the cross-sections are obtained. The variations of the deflection with the param- eters of geometric and gradient of the materials changing along the axial coordinate are examined.