The Dielectric Elastomer-based Minimum Energy Structures (DEMES) pertain to an equilibrium configuration attained by the assembly of a pre-stretched electroactive polymer film and a compliant boundary frame. Because of their unique characteristics, such as fast response and a large reversible stroke; DEMES have been used widely in the development of soft robotic transducers. However, their utility is typically restricted because of the warping resulting from anticlastic curvature. The present investigation examines the effectiveness of stiffeners in controlling this warping, as well as their effect on the resulting electromechanical response when the DEMES is driven electrically. To this end, we devise an energy-based analytical model that predicts the initial equilibrium configuration of an elementary rectangular DEMES with a finite number of stiffeners adhered to the boundary frame. The proposed framework uses the neo-Hookean hyperelasticity model for the polymer film and the linear elastic constitutive model for both the frame and the stiffeners. Predictive capability of the proposed analytical model is established through comparisons with 3D finite element simulations and experimental observations. The analytical model is then extended in the setting of the least-action principle to investigate the complex nonlinear dynamic behavior of the DEMES emanating from the interplay between material and geometric nonlinearities. The proposed dynamic model provides crucial insights into the role of varying levels of geometric and material parameters on the attainment of the initial equilibrium configuration of DEMES and its DC dynamic response when driven by a Heaviside electric load. In particular, we highlight the favorable impact of adding stiffeners in enhancing the stroke of the DEMES and an amplification in the attained equilibrium angle with an increasing spacing between the stiffeners. The analytical model and the results reported in this investigation can be of potential use in pre-designing the geometrical and material properties of DEMES for enhancing its electromechanical performance.