An innovative layout design methodology for stiffened plate/shell structures by material increasing criterion

The motivation of this paper is to develop a new and straightforward approach to provide a topology optimization solution for the layout design of stiffened plate/shell structures. Inspired by the similarities between the branching patterns in nature and stiffener layout patterns in engineering, a so-called material increasing design concept is first introduced to represent the topology configuration of the stiffened plate/shell structures. In addition, a well-founded mathematical explanation for the principles, properties, and mechanisms of adaptive growth behaviors of branching patterns in nature is derived from the Kuhn-Tucker conditions, leading to a novel optimality criterion which can serve engineering purposes for stiffener layout design. In this criterion, the common growth mechanism is described as an ideal 'balanced point' among individual branches in terms of their weight distribution. After characterizing the relationship between the growth behavior and mechanics self-adaptability, the reproduction of branching patterns in nature is implemented by a global coordinative model, which consists of several bottom programming models to find the optimal height distributions of individual branches and a top programming model to play a global coordinative role among them. The benefit and the advantages of the suggested method are illustrated with several 2D examples that are widely used in the recent research of topology optimization.