<p>The contact state of surfaces significantly influences the dynamic properties of assemblies, where the contact area is the key parameter to describe the contact state of assemblies. To address the computational challenges associated with contact area distribution, an improved nominal contact area distribution model is proposed for accurately characterizing the contact state of surfaces. Based on the distribution pattern of contact area, a cumulative quantity function for nominal contact area in logarithmic form is established. And its superiority is proved by comparing with two traditional functions. Based on this, a fractal dimension conversion formula was derived to equate the contact of two rough surfaces to the contact of single rough surface, thereby the optimized expression for the nominal contact area distribution function is obtained. The proposed model is verified through actual contact analysis of the anchorage system (anchor plate and anchor base plate). The results show that the proposed cumulative quantity function for nominal contact area and equivalent fractal dimension function exhibit excellent fitting accuracy and feasibility. In the contact between two rough surfaces, the surface with the smaller fractal dimension dominates the contact behavior. The effectiveness and applicability of the proposed model in complex contact problems are verified through case studies. This research provides new theoretical tools for multiscale mechanical analysis of complex contact surfaces, which has important application value in these fields such as precision manufacturing and tribological optimization.</p>