The Influence of Lateral Boundary Conditions on the Asymptotics in Thin Elastic Plates

This paper is the second in a series of two in which we care about the asymptotics of the three-dimensional displacement field in thin elastic plates as the thickness tends to zero. In Part I we have investigated four types of lateral boundary conditions when the transverse component is clamped. In this Part II we study four other types of lateral conditions when the transverse component is free. We prove that the displacement admits an infinite expansion which can be cut off at any order with optimal error estimates. We describe the first terms in this expansion, namely the first two Kirchhoff-Love displacements and the first boundary layer term. In contrast with the first four lateral conditions, the second Kirchhoff-Love displacement is purely bending and the first boundary layer term is also of bending type and has only one non-zero component (the in-plane tangential).