A new C⁰ 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) cases. There are two major innovations in the present formulation. First, the independent nodal rotation degrees of freedom (DOFs) are employed to enhance the standard 3D isoparametric interpolation for obtaining the displacement and strain test functions, as well as to approximatively design the physical rotation field for deriving the curvature test function. Second, the equilibrium stress functions instead of the analytical functions are used to formulate the stress trial function whilst the couple stress trial function is directly obtained from the curvature test function by using the constitutive relationship. Besides, the penalty function is introduced into the virtual work principle for enforcing the C¹ continuity condition in weak sense. Several benchmark examples are examined and the numerical results demonstrate that the element can simulate the size‐dependent mechanical behaviors well, exhibiting satisfactory accuracy and low susceptibility to mesh distortion.

中文翻译：

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具有旋转自由度的8节点六面体非对称元件，可改善耦合应力弹性

一种新的Ç ⁰ 8节点48-DOF六面体元件被用于在改性偶应力理论的上下文尺寸相关问题的分析开发通过扩展的方法在我们最近的工作（提议Shang等人，诠释J NUMER方法主机119（9）：807‐825，2019）到三维（3D）案例。目前的配方有两个主要的创新。首先，采用独立的节点旋转自由度（DOF）来增强标准3D等参插值以获得位移和应变测试函数，并近似设计物理旋转场以导出曲率测试函数。其次，用平衡应力函数代替解析函数来拟定应力试验函数，而使用本构关系直接从曲率试验函数获得耦合应力试验函数。此外，惩罚函数被引入到虚拟工作原理中以强制执行C ¹弱连续性条件。检验了几个基准示例，数值结果表明，该元件可以很好地模拟尺寸相关的机械行为，显示出令人满意的精度和较低的网格变形敏感性。