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The double-V micro-structures (DVMS) are a type of auxetic materials showing the negative Poisson’s ratio which can contract under compression different from the conventional materials. Due to the unique properties, it can have higher stiffness and better impact resistance with lightweight. In this paper, a cylindrical honeycomb tube based on the double-V unit cell is proposed. Firstly, the nominal Poisson’s ration and Young’s modulus in the longitudinal and circumferential directions are derived analytically. The effect of the geometry parameters of the DVMS tube on the mechanical properties is studied thoroughly. Also, the effect of the width in the radial direction on these mechanical properties is analyzed. Secondly, the finite element (FE) method is utilized to obtain the numerical solutions and verify the accuracy of the analytical solutions. The results show that there is a good agreement between the results obtained by the two methods when the width is smaller enough.

The shape and topology optimization method using a homogenization method is a powerful design tool because it can treat topological changes of a design domain. This method was originally developed in 1988 [1] and have been studied by many researchers. However, their scope of application in real vehicle design works has been limited where a design domain and boundary conditions are very complicated. The authors have developed a powerful optimization system by adopting a general purpose finite element analysis code. A method for treating vibration problems is also discussed. A new objective function corresponding to a multi-eigenvalue optimization problem is suggested. An improved optimization algorithm is then applied to solve the problem. Applications of the optimization system to design the body and the parts of a solar car are presented.