Growth of an Elastic Rod Perfectly Bonded to a von Kármán Elastic Surface

An elastic rod is perfectly bonded to a von Kármán elastic plate such that, except for a relative twist, no relative displacements are allowed between the rod and the plate. The deformation of the confined rod is strongly coupled to that of the flexible environment to which it has to necessarily confirm. A framework is developed where, for a given distribution of growth strains in the rod, the shape as well as the internal forces and the internal moments of the rod-plate system can be determined. The nature of mechanical interaction between the rod and the plate is discussed in detail. The boundary-value-problems, to be solved for a scalar stress function and a scalar transverse displacement field, both piecewise-smooth in the plate domain, include in-plane strain compatibility conditions and transverse force equilibrium equations on, and away from, the curve of rod-plate intersection.