ABSTRACT
ABSTRACT: A Lagrangian approach was developed, which is a mixed method, where in addition to the displacements, the stress-resultants and other variables of state are primary unknowns. This formulation consists of two sets of equations: equilibrium and compatibility of displacement rates (velocities), while its primary unknowns are forces and velocities. For numerical solution, a discrete variational integrator is derived starting from the weak formulation. This integrator inherits the energy and momentum conservation characteristics. The integration of each step is a constrained minimization problem and it is solved using an Augmented Lagrangian algorithm. In this chapter, details of the formulation and computational algorithms are presented, as well as the examples of a simple structure and a sixteen-story building emphasizing on convergence and computational efficiency issues.
