The application of computer animation in the field of publicity animation design provides a simulation platform for the visualization of scientific computing and the dynamic simulation of physical and chemical phenomena. The short time of animation in the promotional video requires designers to have design ideas that fit the theme and precise design positioning. Therefore, designers need to start with creativity and find their own elements and selling points. In order to improve the design effect of publicity animation samples, this study proposes a two-person interaction behavior recognition algorithm based on the interaction relationship hypergraph convolution model, designs an interaction relationship matrix to represent the structure of the interaction relationship graph, and constructs a publicity animation sample design system combined with dynamic simulation technology. Through the experimental analysis, we can see that the method of publicity animation sample design combined with dynamic simulation technology proposed in this paper has good practical effect.