From Truss-Like Continua to Topology Optimum Trusses

Michell’s theory revealed the character of truss-like continua for topological optimal structures. However, because the truss-like continuum structures are not suitable to apply in engineering, they are adopted rarely in structural optimization. Most researchers prefer to obtain the isotropic perforated plate [1]. To obtain uniform perforated plate, the intermediate densities are suppressed generally. This causes numerical instability. The continuous approximation of material distribution is an effective method to overcome this problem [2]. The truss-like continua, as anisotropic material, can be achieved by the free material optimization. However, it is difficult to transfer such continuous structures to manufactable structures properly [3]. This is a significant problem in structural topology optimization. In this paper, we optimize structural topology by transferring the truss-like continua to discrete trusses. The truss-like continua are established by finite element method. The material models are constructed carefully so as to simulate the truss-like continua. The field of continuous distribution of members is determined with the aid of finite element analysis. As there are an infinite number of members, including concentrated and distributed members, from truss-like continua, we need choose finite number of members from them reasonably. All concentrated members should not be omitted. The space between distributed members should be determined properly. According to equilibrium condition, the point, acted by a point load (including supports), should arrange members. The distributed members should be arranged along the curving members in the transverse orientation of the curving members. Several discrete Michell trusses are established by this method.