Yield-stress based error indicator for adaptive quasi-static yield design of structures

•We present an efficient h-adaptive FE analysis procedure for yield design.•A simple error indicator based on these localized yield stresses was proposed.•The non-linear yield criteria is formulated as quadratic conic constraints.•Examples show that the proposed adaptive method is simple and computational efficiency.

Error indicator plays an essential role in developing automatically adaptive analysis procedures that can maximize the rate of convergence of the approximation. For direct limit state analysis problems, the accuracy of numerical solutions is highly affected by local singularities arising from localized yield stresses. It turns out that these local singularity regions should be refined in computational process, making sure that errors in the stress fields can be reduced. In this paper, an error indicator based on the localized yield stresses for adaptive quasi-static yield design of structures will be described. The non-linear yield criterion is formulated as a quadratic conic constraint, allowing that the obtained optimization problem can be solved using highly efficient solvers. Various numerical examples are examined to illustrate the performance of the proposed adaptive procedure.