基于等几何有限元法的功能梯度板自由振动分析

Free vibration analysis of functionally graded plates using isogeometric finite element method

基于一阶剪切变形板理论,建立了分析金属-陶瓷功能梯度板自由振动问题的非均匀有理B样条(NURBS)等几何有限元格式。功能梯度板材料属性沿厚度方向呈梯度连续变化。采用等几何有限元法,讨论了梯度指数、边界条件及长厚比对四种典型功能梯度材料(Al/Al2O3、Al/ZrO2、Ti-6Al-4V/Aluminum oxide和SUS304/Si3N4)板自振频率的影响。数值算例表明,等几何有限元法具有高精度和高收敛率优点,能有效求解功能梯度板的动响应。

Based on the first order shear deformation plate theory, the formulas of isogeometric finite element based on non-uniform rational B- Splines （NURBS） basis functions were derived to study free vibration characteristics of metal/ ceramic functionally graded plates. The material properties were assumed to be graded only in the thickness direction. Four typical functionally graded plates composed of Al/AlzO3, Al/ZrO2, Ti - 6A1 - 4V/Aluminum oxide, and SUS304/ Si3N4 , respectively were studied. The in fluences of gradient index, boundary contition and plate length-to-thickness ratio on the natural frequencies of the functionally graded material plates were investigated in detail. Numerical examples showed that the accuracy and the convergence rate of the isogeometric finite element method are high, and tie method can effectively solve the dynamic response of functionally graded plates.