Enhanced method for the nonlinear structural analysis based on direct energy principles

Numerical methods have become indispensable in the design and analysis of civil engineering structures. In addition to stiffness-based approaches such as the classical Finite-Element-Method, alternative calculation methods for mapping the structural load-bearing and deformation behavior can also be used. Direct energy methods in combination with mathematical optimization algorithms allow the determination of nonlinear deformation states without the need for an incremental calculation due to convergence finding. However, previous implementations of these methods were often limited to comparatively less complex problems with a small amount of degrees of freedom due to numerical inefficiencies. In this article, an enhancement for the previous algorithms for the nonlinear analysis of civil engineering structures based on direct energy principles is introduced. The approach is based on the assumption, that plasticizations often occur only in limited areas of load bearing structures, while large areas can be treated as linear elastic. Thus, the numerical performance can be significantly increased by the combination of both the nonlinear optimization task for the plasticized areas and the direct stiffness method for the linear elastic areas of the structure. A self-adapting computational algorithm is presented in which elements are gradually transferred from the linear to the nonlinear state. Further, an approach for the mapping of material plasticity is introduced, that allows the direct determination of loading and unloading operations without the need for incremental calculations and without violating the potential character of the extremum task.