论文标题
自动配方和限制分析问题的解决
Automated formulation and resolution of limit analysis problems
论文作者
论文摘要
本手稿介绍了一个以非常一般的方式自动化限制分析问题的框架。该框架依赖于特定于Fenics领域的语言以及在圆锥编程设置中的材料强度标准及其相应的支持功能的表示。有限元离散化的各种选择，包括不连续的Galerkin插值，由Fenics提供，使得能够制定下限平衡元素或包括不连续性在内的上限元素。相应优化问题的数值分辨率由内点求解器\ texttt {Mosek}实现，该{Mosek}利用了收益标准的圆锥表示。通过各种说明性示例，从经典的连续性限制分析问题到通用的机械模型，例如板，壳，应变梯度或cosserat Continua，我们表明只能使用几行代码来提出限制分析问题，并以非常简单的方式离散，并非常有效地解决。本文伴随着实现上述框架的Fenics工具箱。
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.
