Stiffener layout design for plate structures by growing and branching tree model (application to vibration-proof design)

From the inspiration of branching systems in nature, this paper suggests a new and direct topology optimization method for the generation of stiffener layout patterns for plate structures by introducing the growing and branching tree model. The growth technique begins with the growing of ground baby stiffeners around a given set of seeds. Each stiffener extends by obeying growing and branching rules like those for trees. A potential for branching is assigned to stiffeners whose cross-sectional areas are greater than a specified threshold dimension, and the best growing direction of a branch is selected depending on the effect of the extension of a new branch. During the growing of a stiffener, the volume growth rate is controlled so as to make it possible to create new branches and to eliminate degenerated stiffeners. The growing process stops when the stiffener volume reaches a given upper limit. Some numerical examples are used to illustrate the effectiveness of the proposed method, and the influence of various factors on the method is discussed.