A geometrically exact nonlinear iso-parametric \(\mathrm {G}^1\)-conforming finite element formulation for the analysis of Kirchhoff rods, based on the cubic Bézier curve interpolation, is presented. In this work, the formulation is restricted to the planar 2D case. Introducing the \(\mathrm {G}^1\)-map, the interpolation preserves the continuity requirement during the deformation process of the rod. In this way, the \(\mathrm {G}^1\)-conformity is implicitly accounted at the element formulation level.

中文翻译：

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等参$$ \ pmb {\ mathrm {G} ^ 1} $$ G 1-有限元用于Kirchhoff杆的非线性分析。第一部分：二维案例

提出了基于三次贝塞尔曲线插值的几何精确的非线性等参\（\ mathrm {G} ^ 1 \）-符合有限元公式，用于分析基尔霍夫棒。在这项工作中，配方仅限于平面2D情况。引入\（\ mathrm {G} ^ 1 \）- map，该插值保留了杆变形过程中的连续性要求。这样，\（\ mathrm {G} ^ 1 \）- conformity在元素公式化级别被隐式考虑。