In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.

Numerical analysis of robustness assessment of steel planar framed structures under sudden external column removal is presented. The analysis is based on the previous experimental and numerical analyzes conducted in the Ph.D. project.Advanced and validated finite element models of steel structures with bolted end plate joints were used using Abaqus software. Six different cases of analysis using flush and extended bolted end-plate joints were performed. The actual results of the axial forces and rotations of the joints, failure models, and other important factors about structure behaviour are presented. The clear division of the results obtained depended on the type of joint used in the structure. In the cases of application of extended end-plate joints in frame analysis, the required level of robustness was reached in all cases and stopping of collapse development was obtained. In all cases of frame analysis with flush end-plate joints, an insufficient level of robustness on progressive collapse was obtained and partial failures of the structures were reached. Due to the location of the external column, the catenary actions to mitigate progressive collapse were very limited.