Unified energy optimization for finite elements simulating elasto-plastic analysis

Elasto-plastic finite element analysis of structural behaviour based on incremental iterative methods is not a trivial task and often involves comprehensive numerical calculations with no guarantee of convergence. An alternative to this approach is the minimization of complementary or potential energy applying powerful and stable solvers for convex optimization which may provide the solution to a given monotonic loading situation in one step for a non-linear hyper-elastic material and thereby simulate an elasto-plastic material behaviour. With weak formulations of equilibrium and compatibility the present novel formulation of the two minimization approaches is demonstrated to be each other’s dual producing identical optimal solutions, and the interpretation of dual parameters is evident. The present unified mixed solution renders accurate results for stresses, strains and displacements which in general are superior to results obtained by strict complementary or potential energy methods. Validation and introductory plane structural examples for both steel and reinforced concrete structures are given and show fast convergence. Furthermore, a comprehensive structural example of the modeling of a reinforced concrete beam is provided and shows convincing results.