  We generalize the F\"{o}ppl-von K\'arm\'an equations to an initially
precurved sheet and present the underlying derivation. A geometrically computed
moment of strain replaces the notion of bending moment and results in a
geometric formulation of the theory of shells. As the curvature approaches
zero, i.e., the sheet becomes flat, the new equations reduce to the classic
F\"{o}ppl-von K\'arm\'an ones. The present theory solves the long-standing
problem of formulating these equations for an a priori curved shell and
applies, for instance, both to shell theory and to strongly curved biomembranes
of cells as closed surfaces, exhibiting crumpling as the membrane thickness
goes to zero.
