Numerical collapse simulation of large-scale structural systems using an optimization-based algorithm

A new algorithm for nonlinear dynamic simulation of structures is presented. The algorithm is based on a mixed Lagrangian approach described by Sivaselvan and Reinhorn (J. Eng. Mech. (ASCE) 2006; 12(8):795-805). The algorithm developed in this paper is for the simulation of large-scale structural systems. The algorithm is applicable to a wide class of structural systems whose constituent material or component behavior can be derived from a stored energy function and a dissipation potential. The algorithm is based on the fact that for such systems, when using a certain class of time-discretization schemes to numerically compute the system response, the incremental problem of computing the system state at the next sample time knowing the current state and the input is one of convex minimization. As a result, the algorithm possesses excellent convergence characteristics. It is also applicable to geometric nonlinear problems. The implementation of the algorithm is described, and its applicability to the collapse analysis of large-scale structures is demonstrated through numerical examples.