<p>This paper presents a density-based Topology Optimization (TO) approach to design structures with controlled intrusion under a given collision involving contact. The collision is equivalent to a design-dependent static load case that can generate linearized responses consistent with collision ones. A continuous transformation from design variables to a crash simulation model is proposed to achieve more accuracy collision responses for grayness topologies, while avoiding mesh distortion and disconnection to guarantee numerical stability. An equivalent load case is reconstructed based on the weighted collision displacement along time, by which the collision loading process can be represented by a single load case without constructing frame-by-frame load cases in a traditional way. An intrusion-rate weighted scheme is used to more effectively represent the collision process where the distribution of the contact load greatly changes over time. Under the equivalent case, a static displacement constraint is developed to indirectly control the maximum intrusion through an adaptive threshold. By using the proposed approach, crash design problems with various contact forms can be robustly solved and the optimized designs exhibit superior intrusion resistance than those by the traditional approach. Numerical examples are discussed to demonstrate the effectiveness and applicability of the proposed approach.</p>