Abstract In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with the strain smoothing technique. Within this framework, the dilatation strain is projected onto the linear approximation space, thus resulting in a purely displacement based formulation. The stability is ensured by enhancing the displacement field with bubble basis functions. The salient features of the proposed method are two fold: the VANP alleviates the locking phenomenon and the strain smoothing suppresses the need to compute the derivative of the basis functions, thus reducing the computational burden. Various benchmark problems in two and three dimensions are numerically solved to demonstrate the robustness, accuracy and the convergence properties of the proposed framework.

中文翻译：

---

星形凸多面体上的 MINI 元素

摘要 在本文中，我们将三角形上的 MINI 元素的概念扩展到星形凸任意多面体。这是通过在多胞体上采用体积平均节点投影 (VANP) 方法结合应变平滑技术来实现的。在这个框架内，膨胀应变被投影到线性近似空间上，从而产生一个纯粹基于位移的公式。通过用气泡基函数增强位移场来确保稳定性。所提出方法的显着特点有两个：VANP 减轻了锁定现象，应变平滑抑制了计算基函数导数的需要，从而减少了计算负担。对二维和三维的各种基准问题进行了数值求解以证明其鲁棒性，