Orthotropic materials or composites are challenging to model due to different elastic properties in two in-plane directions, which requires sufficient mesh refinement to attain desired accuracy. In this regard, an accurate and efficient incompatible graded element is developed for modeling orthotropic functionally graded materials. Properties of Graded finite elements such as Young’s moduli (E11, E22), shear modulus (G12) and Poisson’s ratio (v12) vary. A new incompatible graded element is developed using user subroutines in Abaqus and are compared to available exact solutions. In this study, performance (QM6) graded element is compared with lower-order and higher-order compatible elements (Q4 and Q8) as well as linear triangular (T3) and quadratic triangular (T6) elements with aid of several numerical examples. Additionally, orthotropic graded plate with carbon fibers properties as well as a circular disc with orthotropic properties under internal pressure is included. Furthermore, a curved beam with radially graded properties under the bending moment is studied. Additionally, the performance of various graded elements is compared with analytical solutions using Russell error.

正交各向异性材料或复合材料由于在两个面内方向上的不同弹性特性而难以建模，这需要足够的网格细化才能获得所需的精度。在这方面，开发了一种精确而有效的不相容的梯度元素，用于对正交各向异性功能梯度材料进行建模。诸如杨氏模量（E11，E22），剪切模量（G12）和泊松比（v12）等渐变有限元的属性会有所不同。使用Abaqus中的用户子例程开发了一种新的不兼容的渐变元素，并将其与可用的精确解决方案进行了比较。在这项研究中，借助几个数值示例，将性能（QM6）渐变元素与低阶和高阶兼容元素（Q4和Q8）以及线性三角形（T3）和二次三角形（T6）元素进行了比较。另外，包括具有碳纤维特性的正交各向异性渐变板以及在内部压力下具有正交各向异性特性的圆盘。此外，研究了在弯矩作用下具有径向渐变特性的弯曲梁。此外，将各种渐变元素的性能与使用Russell误差的分析解决方案进行了比较。