Abstract

Geometrically nonlinear and elastoplastic behavior of a circular FGM (functionally graded material) plate under mechanical loading–unloading condition is investigated employing three-dimensional finite element method (FEM) modeling. The through-thickness material distribution of the FGM plate is defined by a power-law variation. The elastic mechanical properties and the elastoplastic material behavior of the FGM plate described respectively by the Mori–Tanaka scheme and the TTO (Tamura–Tomota–Ozawa) model are implemented in the FEM model. The FEM model is validated presenting a very good agreement with the studies from the literature. The influences of nonlinearity, especially the elastoplastic and elastoplastic with geometrically nonlinear behavior, load parameter and thickness-to-radius ratio in terms of nonlinearity, and material composition on the mechanical behavior of the FGM plate are examined. The FEM results are evaluated in terms of the permanent central deflection and the plastic equivalent stress distributions of the FGM plate. The results indicate that a considerable difference occurs between the elastoplastic and elastoplastic with geometrically nonlinear behavior of the FGM plate in terms of both the permanent central deflection and the plastic equivalent stress distributions except ceramic-rich composition that has almost a linear–elastic material behavior, and the geometrical nonlinearity becomes an important parameter with increasing load parameter and decreasing thickness-to-radius ratio. The combination of geometrical and material nonlinearities exhibits a significant influence on the nonlinear mechanical behavior of the FGM plate under plastic deformation.

摘要

采用三维有限元法 (FEM) 建模研究了机械加载-卸载条件下圆形 FGM（功能梯度材料）板的几何非线性和弹塑性行为。FGM 板的全厚度材料分布由幂律变化定义。分别用 Mori-Tanaka 方案和 TTO（Tamura-Tomota-Ozawa）模型描述的 FGM 板的弹性力学性能和弹塑性材料行为在 FEM 模型中实现。FEM 模型经过验证，与文献中的研究非常吻合。非线性的影响，特别是弹塑性和具有几何非线性行为的弹塑性，载荷参数和厚度半径比在非线性方面的影响，和材料成分对 FGM 板的机械性能进行了检查。FEM 结果根据永久中心挠度和 FGM 板的塑性等效应力分布进行评估。结果表明，在永久中心挠度和塑性等效应力分布方面，FGM 板的弹塑性和具有几何非线性行为的弹塑性之间存在相当大的差异，除了具有几乎线性弹性材料行为的富含陶瓷的成分，随着载荷参数的增加和厚径比的降低，几何非线性成为重要参数。