Mathematical models for geometric constraints in manufacturing and optimization of design and manufacturing systems
The fictitious physical models for design and manufacturing and the topology optimization
Mathematical models for creations of novel functions and mechanisms ant the topology optimization
Multiscale analysis based on the homogenization method, and the optimal design of metamaterials
We study optimal design methods and their practical applications in mechanical engineering. Additionally, we construct a novel theory for design engineering based on mathematics and informatics beyond the traditional framework. To achieve our aim, we study mathematical physics in mechanical engineering, mathematical modeling for design problems, modeling for geometrical conditions by the partial differential equations, multiscale design problems, and practical design problems.