功能梯度材料厚板的三维弹性分析

Three dimensional elasticity analysis of functionally graded thick plates

基于三维弹性理论给出了功能梯度材料厚板的基本方程,并用有限元软件-Ansys,采用三维各向同性有限单元,按照复合材料层合板模拟均布荷载下的厚板,讨论了四边简支的边界条件,梯度指数和板的厚宽比等因素对板的无量纲挠度以及无量纲应力的影响。三维数值模型给出的挠度和应力分布不同于基于Kirchhoff-Love直法线假设的经典层合板理论给出的挠度和应力分布。

Based on three dimensional elasticity theory, governing equations for the thick plates. Then, analytical solutions for compound material multilayered plates are obtained by using finite element software-Ansys. At last, the solutions for deflections of functionally graded thick plates with various rate between thickness and width and subjected to simply supported boundary conditions are presented. The influence of the material gradient index on the dimensionless deflections is carefully discussed. The displacement and stress distribution of the 3-D numerical model is different from The displacement and stress hypothesis of the classical laminate theory based on the Kirchhoff-Love hypotheses of the straight inextensional normals.