Optimized design of multi-material cellular structures by level-set method with Guyan reduction

Owing to their tailorable physical properties, periodic cellular structures are considered promising materials for use in various engineering applications. To fully leverage the potential of such structures, it will be necessary to develop an optimized design method capable of producing intricate material layouts without sacrificing manufacturability. This paper presents a topology optimization framework for designing manufacturable, multi-material cellular structures that are to be subjected to temperature change. Under this framework, multi-material layouts within designable unit cells are represented using level-set functions and corresponding Boolean operations; by assuming a common length scale between these unit cells and the macrostructure, the manufacturability of optimized designs is guaranteed. Increases in computational cost and storage requirement are minimized by applying the Guyan reduction method, in which the secondary degree of freedom is condensed out to reduce the size of the discretized model. The design capabilities of the proposed method were investigated using several numerical models, with the results demonstrating that the method achieves overall improvements in performance as a result of its expanded design space.

Second-Order Systems With Singular Mass Matrix and an Extension of Guyan Reduction

The set of consistent initial conditions for a second-order system with singular mass matrix is obtained. In general, such a system can be decomposed (i.e., partitioned) into three coupled subsystems of which the first is algebraic, the second is a regular system of first-order differential equations, and the third is a regular system of second-order differential equations. Under specialized conditions, these subsystems are decoupled. This result provides an extension of Guyan reduction to include viscous damping.