The present manuscript presents a framework for automating the formulation and resolution of limit analysis problems in a very general manner. This framework relies on FEniCS domain-specific language and the representation of material strength criteria and their corresponding support function in the conic programming setting. Various choices of finite element discretization, including discontinuous Galerkin interpolations, are offered by FEniCS, enabling to formulate lower bound equilibrium elements or upper bound elements including discontinuities for instance. The numerical resolution of the corresponding optimization problem is carried out by the interior-point solver \texttt{Mosek} which takes advantage of the conic representation for yield criteria. Through various illustrative examples ranging from classical continuum limit analysis problems to generalized mechanical models such as plates, shells, strain gradient or Cosserat continua, we show that limit analysis problems can be formulated using only a few lines of code, discretized in a very simple manner and solved extremely efficiently. This paper is accompanied by a FEniCS toolbox implementing the above-mentioned framework.

中文翻译：

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自动制定和解决极限分析问题

本手稿提供了一个框架，用于以非常通用的方式自动制定和解决极限分析问题。该框架依赖于 FEniCS 领域特定语言和材料强度标准的表示及其在圆锥规划设置中的相应支持功能。FEniCS 提供了各种有限元离散化的选择，包括不连续的伽辽金插值，从而能够制定下界平衡元素或上界元素，例如包括不连续性。相应优化问题的数值求解由内点求解器 \texttt{Mosek} 执行，它利用了屈服准则的圆锥表示。通过从经典连续极限分析问题到广义力学模型（如​​板、壳、应变梯度或 Cosserat 连续体）的各种说明性示例，我们表明可以仅使用几行代码来制定极限分析问题，并以非常简单的方式进行离散化并且非常有效地解决了。本文附有一个实现上述框架的 FEniCS 工具箱。