Abstract
In recent years, the functionally graded materials (FGM) with cellular structure have become a hot spot in the field of materials research. For the continuously varying cellular structure in the layer-wise FGM, the connection of gradient cellular structures has become the main problem. Unfortunately, the effect of gradient connection method on the overall structural performance lacks attention, and the boundary mismatch has enormous implications. Using the homogenization theory and the level set method, this article presents an efficient topology optimization method to solve the connection issue. Firstly, a simple but efficient hybrid level set scheme is developed to generate a new level set surface that has the partial features of two candidate level sets. Then, when the new level set surface is formed by considering the level set functions of two gradient base cells, a special transitional cell can be constructed by finding the zero level set of this generated level set surface. Since the transitional cell has the geometric features of two gradient base cells, the shape of the transitional cell fits perfectly with its connected gradient cells on both sides. Thus, the design of FGM can have a smooth connectivity with C1 continuity without any complex numerical treatments during the optimization. A number of examples on both 2D and 3D are provided to demonstrate the characteristics of the proposed method. Finite element simulation has also been employed to calculate the mechanical properties of the designs. The simulation results show that the FGM devised by the proposed method exhibits better mechanical performances than conventional FGM with only C0 continuity.
Highlights
Organisms like bamboo, to adapt the environment [1], often consist of a gradient structure.Inspired by the materials that already exist in nature [2], functionally graded materials (FGM) is usually composed of continuously varying cellular structures in one direction and self-repeated in the other direction
FGM is devised by using the proposed transitional cell method, in which the FGM is consisting of cellular base structure (CBS) and transitional cellular structure (TCS)
The results show that the relative difference in the FGM with different connection methods is 8.65%, which means the proposed transitional connection method can greatly increase the stiffness of the optimized FGM
Summary
To adapt the environment [1], often consist of a gradient structure. Level set methods [45], owing to their perfect description of the smooth boundary, are effective ways to divide solid and void parts of the structure in topology optimization This favorable feature of the level set methods makes it to be considered as a favorable candidate to handle the connectivity issue in the topology optimization design for FGMs. The main concept of LSM is to describe a low-dimensional structural geometry with the high-dimensional level set function, and the zero level set represents the structural boundary. The parametric level set methods (PLSM) use the radial basis functions (RBFs) [52] to interpolate the level set function, and the time and spatial variables in the level set function are decoupled In this fashion, the complicated H-J PDE-driven topology optimization problem in the traditional LSM can be converted into a compact parameterized optimization problem, which can be solved by the gradient-based algorithms.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
