Abstract
It is well known that the mechanical behavior of material mainly depends on the geometric properties of the microstructure, such as material distribution, shape or size of the material. It is said that it will be possible to maximize the mechanical performance of a macro-structure, if ‘types or kinds of materials to be mixed or the combinations thereof’ are optimized and ‘the geometric properties of micro-structure’ are optimized. For this reason, the authors have developed topology optimization of microstructure using the general finite element method as a numerical approach. However, the general finite element mesh is not necessary appropriate to express the complicated real material distribution of microstructure and furthermore depends considerably on the initial value of some parameters. Thus, the present study applies a new approach, the phase-field method, to express the complicated topology of microstructure and introduces the formulation to maximize the stiffness of the microstructure with a prescribed material volume under linear elastic regime. For the fundamental research, we firstly start from investigation of the initial value dependency of the present method on the final optimization solution by making use of a series of numerical examples.
