In the present study, a simple four-node high-order shear deformation plate bending element based on modified first-order shear deformation theory has been developed to analyze functionally graded plates subjected to both sinusoidal or uniformly distributed transversal loads. Unlike other high-order shear deformation theories, the number of unknowns has been reduced to five by using the condition of zero transverse shear stress at the free top and bottom surfaces of the FG plate and by the assumption that the transverse shear strains are quadratically distributed through the thickness. The concept of transverse shear stress-energy has been employed to improve the element performance. Furthermore, the assumed natural shear strain technique has been employed to avoid any potential locking phenomenon. Moreover, the principle of minimum total potential energy has been used to derive the elementary stiffness matrix and the loading vector. To avoid the membrane–bending coupling, the concept of the neutral plane has been introduced. The developed finite element has been validated through a set of tests available in the literature.

在本研究中，已经开发了一种基于改进的一阶剪切变形理论的简单四节点高阶剪切变形板弯曲元件，以分析承受正弦或均匀分布的横向载荷的功能梯度板。与其他高阶剪切变形理论不同，通过在FG板的自由顶面和底面使用零横向剪应力的条件以及假设横向剪应变呈二次分布的假设，未知数减少到五个通过厚度。横向剪应力能量的概念已被用来改善元件性能。此外，已采用假定的自然剪切应变技术来避免任何潜在的锁定现象。此外，最小总势能原理已被用来推导基本刚度矩阵和载荷矢量。为了避免膜片弯曲的耦合，引入了中性面的概念。开发的有限元已经通过文献中提供的一组测试进行了验证。