Large language models (LLMs) are establishing new paradigms for engineering applications by enabling natural language control of complex computational workflows. This paper introduces FeaGPT, the first framework to achieve complete geometry-mesh-simulation workflows through conversational interfaces. Unlike existing tools that automate individual FEA components, FeaGPT implements a fully integrated Geometry-Mesh-Simulation-Analysis (GMSA) pipeline that transforms engineering specifications into validated computational results without manual intervention. The system interprets engineering intent, automatically generates physics-aware adaptive meshes, configures complete FEA simulations with proper boundary condition inference, and performs multi-objective analysis through closed-loop iteration. Experimental validation confirms complete end-to-end automation capability. Industrial turbocharger cases (7-blade compressor and 12-blade turbine at \SI{110000}{rpm}) demonstrate the system successfully transforms natural language specifications into validated CalculiX simulations, producing physically realistic results for rotating machinery analysis. Additional validation through 432 NACA airfoil configurations confirms scalability for parametric design exploration. These results demonstrate that natural language interfaces can effectively democratize access to advanced computational engineering tools while preserving analytical rigor.