On a von Kármán System for Anisotropic Viscoelastic Plates

Abstract

We deal with a nonlinear system of equations describing the in-plane displacements and the deflection of the anisotropic viscoelastic plate made of a long memory material acting under the perpendicular load. We derive the full von Kármán system for the in-plane displacements and the deflection of the middle surface of the plate. The system contains the nonlinear integropartial differential operators applied to the in-plain strain tensor and to the tensor product of the displacement gradients. If the right-hand side of the system fulfils some estimate then the existence of a weak solution can be derived using the Rothe's method.