A Mathematical Modeling for Plastic Analysis of Planar Frames by Linear Programming and Genetic Algorithm

In this paper, a mathematical modeling is developed for plastic analysis of planar frames. To this end, the researcher tried to design an optimization model in linear format in order to solve large scale samples. The computational result of CPU time requirement is shown for different samples to prove efficiency of this method for large scale models. The fundamental concept of this model is obtained from moment distribution method which is a safe theorem based method, so in this mathematical modeling, the objective is finding the largest load which ensures equilibrium and yield conditions. Contrary to moment distribution method, calculation of load factor and the value of moments in the elements are completely automatic and not to need user decision. As the objective function and constraints of this model are linear so it can be solved by linear programming (LP) software such as LINGO that is shown in this paper and also the model is solved by genetic algorithm (GA) to compare two solutions