Chalal Hocine, Abed-Meraim Farid
Laboratory LEM3, Université de Lorraine, CNRS, Arts et Métiers ParisTech, F-57000 Metz, France.
Materials (Basel). 2018 Jun 20;11(6):1046. doi: 10.3390/ma11061046.
In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.
在本论文中，提出了棱柱形和六面体二次实体⁻壳（SHB）有限元，用于对功能梯度材料（FGM）制成的薄结构进行几何非线性分析。所提出的SHB有限元是在纯三维框架内开发的，位移是唯一的自由度。此外，面内降阶积分技术与假定应变法相结合，以减轻各种锁死现象。此外，沿着代表厚度的特殊方向设置任意数量的积分点。所开发的单元与功能梯度特性相结合，用于模拟薄FGM板。为此，假定FGM板的杨氏模量根据体积分数分布在厚度方向上逐渐变化。所得公式在大位移和大旋转框架下被实现到准静态ABAQUS/Standard有限元软件中。考虑了一些常见的非线性基准问题，以评估所提出的SHB单元的性能和精度。与文献中的参考解进行比较，证明了所开发的SHB单元在薄FGM板三维模拟方面的良好能力。
