The process of opinion expression and exchange is a critical component of democratic societies. As people interact with large language models (LLMs) in the opinion shaping process different from traditional media, the impacts of LLMs are increasingly recognized and being concerned. However, the knowledge about how LLMs affect the process of opinion expression and exchange of social opinion networks is very limited. Here, we create an opinion network dynamics model to encode the opinions of LLMs, cognitive acceptability and usage strategies of individuals, and simulate the impact of LLMs on opinion dynamics in a variety of scenarios. The outcomes of the simulations inform about effective demand-oriented opinion network interventions. The results from this study suggested that the output opinion of LLMs has a unique and positive effect on the collective opinion difference. The marginal effect of cognitive acceptability on collective opinion formation is nonlinear and shows a decreasing trend. When people partially rely on LLMs, the exchange process of opinion becomes more intense and the diversity of opinion becomes more favorable. In fact, there is 38.6% more opinion diversity when people all partially rely on LLMs, compared to prohibiting the use of LLMs entirely. The optimal diversity of opinion was found when the fractions of people who do not use, partially rely on, and fully rely on LLMs reached roughly 4:12:1. Our experiments also find that introducing extra agents with opposite/neutral/random opinions, we can effectively mitigate the impact of biased/toxic output from LLMs. Our findings provide valuable insights into opinion dynamics in the age of LLMs, highlighting the need for customized interventions tailored to specific scenarios to address the drawbacks of improper output and use of LLMs.