The main contribution of this study is the development of an efficient element in modeling thin to thick functionally graded (FG) square plates. To accomplish this goal, a 3D plate bending element is developed by taking advantages of the mixed interpolation of tensorial components approach (MITC). The recommended element has four nodes with six degrees of freedom at each node. Both higher-order shear deformation and the thickness stretching are considered. A fully 3D constitutive relation is adopted. Utilizing an assumed strain field for transverse normal strain causes the element to perform well, even when the thickness becomes thin. Based on the rule of mixture and Mori–Tanaka scheme, a Voigt model is also employed in this study to represent through the thickness distribution of FG material property. Static, free and force vibration analyses of the square FG plates, with different boundary conditions, are investigated in this paper. Several benchmark problems are studied to demonstrate the ability of the element in the static and dynamic analysis of thin/thick plates. Moreover, the effects of different power index and boundary conditions on the response of plate are also investigated.

这项研究的主要贡献是开发了一种用于建模从薄到厚的功能梯度（FG）方板的有效元件。为了实现这一目标，通过利用张量分量混合混合插值方法（MITC）来开发3D板弯曲元件。推荐元素有四个节点，每个节点有六个自由度。同时考虑了高阶剪切变形和厚度拉伸。采用完全3D本构关系。将假定的应变场用于横向法向应变，即使厚度变薄，也可以使单元发挥良好的性能。根据混合规则和Mori–Tanaka方案，在本研究中还采用了Voigt模型来表示FG材料特性的厚度分布。静态的，本文研究了在不同边界条件下方形FG板的自由振动和力振动分析。研究了几个基准问题，以证明元素在薄/厚板静态和动态分析中的能力。此外，还研究了不同功率指数和边界条件对板响应的影响。