Optimal stiffener layout of plate/shell structures by bionic growth method

A novel design method for stiffener layout of plate and shell structures is proposed in this paper. The method is inspired by the morphogenesis mechanism of dicotyledonous venation which is featured by hierarchy and functional adaptivity. It is expected that a optimal stiffener layout can be gradually achieved if the stiffeners extend by obeying a similar growth rule as the venation. Starting from the so called “seeds”, the stiffeners grow and branch off towards the direction that optimizes the structural performance. And the stiffeners with the minimum effectiveness to the structural performance are degenerated simultaneously. During the design process, the relative density of each element is treated as the design variable. The growth and degeneration of the stiffeners are determined by the nodal and elemental sensitivity numbers respectively. The design algorithm is programmed in Python and integrated with Abaqus software which is used as the FEA preprocessor and solver. To validate the effectiveness of the proposed method, it is applied to design the stiffener layouts of some typical structures with the objective of maximizing the overall stiffness with a volume constraint.

Download Full-text

Multidiscipline Topology Optimization of Stiffened Plate/Shell Structures Inspired by Growth Mechanisms of Leaf Veins in Nature

Mathematical Problems in Engineering ◽

10.1155/2013/653895 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Baotong Li ◽

Jun Hong ◽

Suna Yan ◽

Zhifeng Liu

Keyword(s):

Topology Optimization ◽

Optimization Methods ◽

Optimization Method ◽

Shell Structures ◽

Stiffened Plate ◽

Numerical Studies ◽

Branching Patterns ◽

Leaf Veins ◽

Stiffener Layout ◽

Computational Resources

Biological structures with preeminent performance in nature endow inexhaustible inspiration for creative design in engineering. In this paper, based on the observation of the natural morphogenesis of leaf veins, we put forward a simple and practical multidiscipline topology optimization method to produce the stiffener layout for plate/shell structures. This method simulates the emergence of complex branching patterns copying the self-optimization of leaf veins which always try to grow into a configuration with global optimal performances. Unlike the conventional topology optimization methods characterized by “subtraction mode,” the proposed method is based on the “addition mode,” giving great potential for designers to achieve more clear stiffener layout patterns rather than vague material distributions and, consequently, saving computational resources as well as enhancing availability of design outputs. Numerical studies of both static and dynamic problems considered in this paper clearly show the suitability of the proposed method for the optimal design of stiffened plate/shell structures.

Download Full-text

An Innovative Layout Design Methodology for Stiffened Plate/Shell Structures by Material Increasing Criterion

Journal of Engineering Materials and Technology ◽

10.1115/1.4023781 ◽

2013 ◽

Vol 135 (2) ◽

Cited By ~ 3

Author(s):

Baotong Li ◽

Jun Hong ◽

Zhelin Wang ◽

Zhifeng Liu

Keyword(s):

Topology Optimization ◽

Programming Model ◽

Layout Design ◽

Shell Structures ◽

Mathematical Explanation ◽

Stiffened Plate ◽

Branching Patterns ◽

Stiffener Layout ◽

The Relationship ◽

Stiffener Layout Design

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.

Download Full-text