Topology and size optimization of truss structures based on material density approach and MMA

In this article, MMA which is a mathematical programing method is utilized for solving truss optimization problem. Although this method has been widely used in topology optimization problems of continuous structures, it has received less attention in the case of truss structures. The optimization problem considered here is the problem of minimizing the strain energy of the structure by considering the volume constraint. For the first time, the basics of the SIMP method and the application of the penalty exponent of the density function have been used for simultaneous optimization of topology and size of the truss members.To solve the optimization problem, analytical sensitivity analysis has been performed. Various problems have been solved at the end of the paper and the results have been discussed. The results show that if the appropriate penalty exponent is chosen, the correct optimal solution is obtained for the benchmark problems. Also, some more practical problems have been solved and the results have been discussed.