Design of structures using level set topology optimization and strain energy methods

Level set method (LSM) is a mathematical approach for obtaining structures with specified characterization by moving the interface boundaries between material domain and void domain. This paper used LSM for topology optimization (TO) of a statically loaded structures and also auxetic meta-materials. It is shown that different groups of auxetic structures as very useful materials in many areas, such as the piezoresistive sensor field could be obtained by using level set method. Different groups of auxetic structures obtained by LSM are re-entrant, chiral and some novel auxetic structures that have not been reported before were designed by changing initial design and volume fraction. The scale of production of auxetic structures is in the range of 0.1nm to 10 m and these structures are used in the field of piezoresistive sensors by coating them with ultrafine particles such as nanocarbons. Furthermore, our study revealed that the performance of the code retains the number and direction of symmetries of initial design for final structure. So, auxetic structures with desired symmetries could be designed by using the same symmetries for initial designs.