Based on equilibrium thermodynamics and the Gent hyperelastic model, a coupled electromechanical constitutive model is developed for circular dielectric elastomer membrane actuators under combined internal pressure and voltage. This investigation systematically examines the influence of rigid inclusion size on the electromechanical response, addressing a crucial design parameter for enhancing the performance and reliability of such actuators. The study establishes a complete theoretical framework that connects material behavior with geometric configuration, providing a solid foundation for performance prediction and design optimization. To accurately analyze this electromechanical coupling behavior, the governing nonlinear boundary value problem is solved using the shooting method. This numerical approach effectively handles the coupled mechanical and electrical equilibrium equations through an iterative solution procedure that satisfies all boundary conditions. The methodology enables precise determination of the membrane's deformation field, stress distribution, and electric field characteristics under various inclusion sizes and loading conditions, offering reliable numerical predictions for design purposes. The computational results reveal that the inclusion size predominantly influences the mechanical and electrical response at the inner boundary region. Increasing the inclusion size leads to a notable suppression of the large oscillations in vertical displacement, stretch ratio, and true stress that are typically induced by applied voltage. This suppression effect demonstrates how geometric parameters can be utilized to control the dynamic response of the membrane. Further analysis of the electric field distribution demonstrates that larger inclusions effectively stabilize the electric field near the critical inner boundary while simultaneously enhancing its overall spatial uniformity. These combined effects contribute to a significant increase in the critical electric field strength, thereby substantially delaying the onset of electromechanical instability and improving the operational safety of the device. These findings provide valuable theoretical guidance and practical insights for optimizing the design of high-performance dielectric elastomer actuators. Through appropriate selection of inclusion size, more stable actuation performance can be achieved with reduced stress concentration and improved dielectric strength. The research outcomes offer clear design principles for enhancing device reliability in various engineering applications. The established methodology and obtained results contribute to the development of more reliable dielectric elastomer devices with predictable performance characteristics, providing important references for both academic research and engineering practice.