Topology optimization for minimum stress design with embedded movable holes

Abstract Currently, most works on layout optimization problem of continuum structure embedded with movable holes are all carried out to maximize the stiffness of the overall system. In this work, the embedding problem is solved for minimum stress design for the first time. To this end, we propose an effective hybrid methodology under SIMP-based computational framework. The material density characterizing the topology of the load transfer path and the geometric parameters defining the rigid body motion (translation and rotational) of the embedded holes are considered as design variables and are optimized simultaneously to minimize the aggregated maximum stress. To unite these two seemingly different representations into an optimization model, we mapped the embedded holes into a density field on a fixed grid using a Sigmoid activation function. Then, a new SIMP-like material interpolation scheme that considers embedding holes is introduced for stiffness penalization and stress penalization. The optimization model for solving the minimum stress problem embedded with movable holes and its sensitivity analysis are detailed. Finally, two typical examples are performed to illustrate the effectiveness of the proposed methodology.