功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。

Semi-analytical gradient finite element method for 3D analyses of functionally graded material plates

To combine semi-analytical finite element method with gradient finite element method formed a kind of semi-analytical gradient finite element method for solving the problems of functionally graded material plates.The method has the advantages: both strong adaptability,unified program of finite element method and saving element and calculation of semi-analytical finite element method and adapting to any gradient distribution of gradient finite element method,and realizes the purpose of using 1-D numerical calculation and giving 3-D analysis results.The calculating examples indicated the accuracy,function and the features above expressed,and fully revealed the 3-D distribution of mechanical responses of functionally graded material plates.Semi-analytical gradient finite element method can be extended to various analyses of other functionally graded material face structures.