Automated formulation and resolution of limit analysis problems

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