Local existence and uniqueness for a geometrically exact membrane-plate with viscoelastic transverse shear resistance

We prove the local existence and uniqueness to a geometrically exact, observer-invariant membrane-plate model introduced by the author. The model consists of an elliptic partial differential system of equations describing the equilibrium response of the membrane which is non-linearly coupled with a viscoelastic evolution equation for exact rotations, taking on the role of an orthonormal triad of directors. This coupling introduces a viscoelastic transverse shear resistance. Refined elliptic regularity results together with a new extended Korn's first inequality for plates and shells allow to proceed by a fixed point argument in appropriately chosen Sobolev-spaces in order to prove existence and uniqueness. Copyright (c) 2004 John Wiley & Sons, Ltd.