Clamping apparatus and methods are provided. The apparatus can include a rigid backing member having a plurality of apertures disposed therethrough. The apparatus can further include a spring member having a plurality of radial members each having a first end and a second end. The first end of the radial members can be connected at a hub. The second end of each radial member can be connected to a flange. A plurality of apertures, corresponding to the plurality of apertures in the backing member, can be disposed about the flange. The radial members can be fabricated using two or more plies of resin-impregnated carbon fiber. The spring member can be affixed to the backing member using one or more fasteners disposed in the backing member apertures and corresponding aperture disposed in the flange.