Integrated Topology and Sizing Optimization of Frame Structure with Interstory Drift Ratio, Stability and Non-Intersecting Constraints

Topology optimization has proven effective for achieving reliable designs under specific constraints. However, most existing studies focus on continuum structures, with limited attention given to frame structures despite their widespread use in practice. Motivated by this problem, this paper develops a lightweight optimization method for frame structures that incorporates interstory drift ratio and stability constraints in a cost-effective manner. The novelty of this paper is not only that the deformation control and stability requirements are included into optimization, but also a new non-intersecting constraint is introduced to prevent member crossings in the final design. Moreover, to achieve projection of continuous size variables onto discrete standard members, the ordered solid isotropic material with penalization (SIMP) interpolation is combined with the normalized Heaviside function to project continuous size variables onto discrete standard members. Then, the sensitivities of the constraint functions with respect to topology and size design variables are derived, respectively, and the proposed integrated optimization problem is solved by a nested optimization algorithm. Finally, the proposed methodology is applied to the light-weight design of a 3D tower frame structure to further demonstrate the approach’s feasibility.