An augmented Newton method in elastic-plastic structural optimization

In this paper, an augmented Newton method for the optimization of elastic–plastic structures is proposed. It is shown that the optimization algorithm has to be nested due to the nature of elastic–plastic problems, and in this framework, an e cient and robust algorithm should be developed. For this purpose, the principle of the integrated method is incorporated to enhance the system matrix of the Newton method in the framework of the nested approach. Namely, the system equation is rst derived in the extended space, and then it is condensed. After some manipulation, a compact form of the system matrix equation is derived which is similar to that in the conventional Newton method. The augmentation terms can be evaluated based on the design sensitivities, so the computational cost is about the same as that for the conventional method, but it substantially searches for the solution in the extended space. The potential of the proposed method is exempli ed in a simple elastic–plastic truss