Discrete variational mechanics and associated numerical integrators have seen a major development in recent years. There has been a growing realization that stability of numerical methods can be improved for certain systems by algorithms that are compatible with variational and geometric structures, such as preservation of the symplectic form on phase space and of the momentum maps arising from the symmetries of the system. Discrete mechanics has been developed as a result of the interplay of classical theoretical mechanics, numerical analysis, and computer science, which has become increasingly important in concrete applications. Remarkably, to our knowledge, there is no major application of these discrete mechanics techniques to civil engineering.
The longer term aim of this work is to apply structure preserving algorithms to concrete problems in construction, like thin-shells with irregular surfaces. Our goal in this paper is to provide variational integrators associated with mathematical models of beams and to carry out dynamic and static two-dimensional simulations.