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Modified unified co-rotational framework with beam, shell and brick elements for geometrically nonlinear analysis

用于梁、板壳、体单元几何非线性分析的改进的统一共旋框架

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Abstract

The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis. This paper presents a modified co-rotational framework, unified for beam, shell, and brick elements. A unified zero-spin criterion is proposed to specify the local element frame, whose origin is always located at the centroid. Utilizing this criterion, a spin matrix is introduced, and the local frame is invariant to the element nodal ordering. Additionally, the projector matrix is redefined in a more intuitive way, which is the derivative of local co-rotational element frame with respect to the global one. Furthermore, the nodal rotation is obtained with pseudo vector and instantaneous rotation, under a high-order accurate transformation. The resulting formulations are achieved in unified expression and thus a series of linear elements can be embedded into the framework. Several examples are presented to demonstrate the efficiency and accuracy of the proposed framework for large displacement analysis.

摘要

共旋方法是一种近年来受到广泛关注的技术, 其可将现有的高性能线性单元扩展用于几何非线性分析. 本文提出了一种改进的梁、板壳、体单元统一的共旋框架. 提出了统一零自旋准则来确定原点始终位于单元质心的共旋坐标系. 通过引入自旋矩阵, 共旋坐标系与单元节点顺序无关. 基于共旋坐标系与全局坐标系中变量的关系, 更加直观地定义了投影矩阵. 同时, 单元转动通过伪矢量与瞬时旋转轴之间的高阶转换获得. 本文给出了统一的表达式, 以便于将一系列线性单元应用于求解框架. 给出了几个大位移分析数值算例, 结果表明本文改进的方法具有较高的效率和求解精度.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11972297 and 11972300) and the Fundamental Research Funds for the Central Universities of China (Grant No. G2019KY05203).

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Authors and Affiliations

  1. School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China

    Yufei Rong  (戎宇飞), Qin Sun  (孙秦) & Ke Liang  (梁珂)

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  1. Yufei Rong  (戎宇飞)
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  2. Qin Sun  (孙秦)
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  3. Ke Liang  (梁珂)
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Correspondence to Qin Sun  (孙秦).

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Rong, Y., Sun, Q. & Liang, K. Modified unified co-rotational framework with beam, shell and brick elements for geometrically nonlinear analysis. Acta Mech. Sin. 38, 421136 (2022). https://doi.org/10.1007/s10409-021-09081-x

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