Efficient elasto-plastic modelling of reinforced concrete beams applying convex optimization

In recent years, much attention has been devoted to the concept of Finite Element Limit Analysis (FELA), which combines Finite Elements, rigid-plastic material models, and convex optimization algorithms. While this has resulted in numerical frameworks for limit analysis of reinforced concrete structures that determine the limit load in a quite accurate and efficient manner, the assumption of rigid plasticity prevents the determination of any finite deformations.

In an effort to extend a recently proposed complementary framework for in-plane elasto-plastic analysis of reinforced concrete walls towards shell elements, a finite element framework for elasto- plastic analysis of fully cracked reinforced concrete beams, including axial loading, is investigated. As for the previous work on membrane elements, the framework uses the principle of minimum complementary energy and a hyper-elastic material model to formulate the problem as a convex optimization problem.

The accuracy and computational efficiency of the model are investigated with respect to the number of layers as well as the number of sub-model points per element.