Effects of the Properties of Bi-modulus Material on Stiffness Design

A bi-modulus material, which tension modulus is different from the compression one along the same direction, is widely used in engineering, e.g., concrete or cast iron. For the sake of the mechanical properties of a bi-material depend on local stress state, many times of structural reanalysis are required to obtain the accurate stress field. To improve the efficiency of topology optimization of a structure with bi-modulus material, the reference-interval with material replacement method is used and the effects of the mechanical properties of bi-material on the final material distribution of a structure are discussed. In the method, a reference interval of strain energy density (SED) is adopted to control the update of design variables. The interval changes frequently in iterations to satisfy the active constraints in optimization. On the other hand, a material-replacement scheme in which the bi-modulus material is replaced with two types of isotropic materials is suggested to simplify structural analysis. And then, the effective SED field of the structure with original material is obtained according to the stress and strain fields of the structure with replaced materials and the update of design variables can be carried out by comparing the local effective SED and the current reference interval of SED. Numerical results show that the difference between the tension modulus and the compression one of the bi-modulus material in a structure has obvious effects on the final material distribution, which is important for an engineer to find an appropriate initial design in practical engineering.