We present an efficient approach to compute the matrices used in finite element formulations where self‐equilibrated (zero divergence) approximations of the stress field are used. The fundamental aspect of this approach is that it is applicable to polynomial approximations of high degree (it was tested up to degree 10), providing closed‐form expressions for the elementary matrices involved. The components of the stress field are defined as a function of the coordinates in the master element, facilitating the postprocessing of the finite element results and allowing for the consideration of geometric parameters in reduced order models.

中文翻译：

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二维弹性中基于应力的有限元逼近的有效方法

我们提出了一种有效的方法来计算有限元公式中使用的矩阵，其中使用了应力场的自平衡（零散度）近似值。该方法的基本方面是，它适用于高阶多项式逼近（已测试至10级），为涉及的基本矩阵提供了封闭形式的表达式。应力场的分量是根据主元素中的坐标定义的，从而有利于有限元结果的后处理，并允许在降阶模型中考虑几何参数。