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In rigid plastic analysis one of the most widely applicable methods that is based on the minimum principle, is the combination of elementary mechanisms which uses the upper bound theorem. In this method a mechanism is searched which corresponds to the smallest load factor. Mathematical programming can be used to optimize this search process for simple frames, and meta-heuristic algorithms are the best choice for larger frame structures. In this paper, the Colliding Bodies Optimization (CBO) and its enhanced variant (ECBO) are employed to optimize the process of finding an upper bound for the collapse load factor of the planar frames. The efficiency of these algorithms is compared to that of the Particle Swarm Optimization (PSO) algorithm through four numerical examples form multi-bay multi-story frames and pitched roof frames.

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One of the goals of the nonlinear structural analysis is to reduce the required time for obtaining the numerical solution. More important than this issue, the nonlinear scheme could converge to the answers for all types of problems. A perfect nonlinear solver must have both of these specifications. This article aims to reduce the duration of structural analysis as well as to boost convergent requirements. To reach these two objectives, the authors simultaneously minimize the kinetic and residual structural energies. The ability of the new formulation is shown by solving several structures, with nonlinear geometrical behavior.  Based on the compressive studies, numerical solutions show the high efficiency of the new method.