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Geometry design can improve a capacitive radio-frequency microelectromechanical system switch's reliability by reducing the impacts of intrinsic biaxial stresses and stress gradients on the switch's membrane. Intrinsic biaxial stresses cause stress stiffening, whereas stress gradients cause out-of-plane curling. We use topology optimization to systematically generate designs, by minimizing stress stiffening, minimizing curling, or minimizing stress stiffening while constraining the curling behavior. We present the corresponding problem formulations and sensitivity derivations and discuss the role of key elements in the problem formulation.