Statics of hybrid structures composed of interacting membranes and strings

The equations governing large deformations of hybrid structures are derived from basic principles of mechanics. The considered structures comprise membrane elements with strings arranged inside and possibly along boundaries of the entire structure. No special assumptions are imposed on the mechanical properties of membrane and string elements. The principle of virtual work is formulated under weak continuity hypotheses so that the derived theory takes into account general types of membrane-string attachments. The theory of mechanical constitutive equations for the considered structures is developed and the form of elastic constitutive equations is discussed. A number of specific aspects of string-membrane interactions are analyzed and possible applications of the developed theory are indicated.