  A simple skew-symmetric Nitsche's formulation is introduced into the
framework of isogeometric analysis (IGA) to deal with various problems in small
strain elasticity: essential boundary conditions, symmetry conditions for
Kirchhoff plates, patch coupling in statics and in modal analysis as well as
Signorini contact conditions. For linear boundary or interface conditions, the
skew-symmetric formulation is parameter-free. For contact conditions, it
remains stable and accurate for a wide range of the stabilization parameter.
Several numerical tests are performed to illustrate its accuracy, stability and
convergence performance. We investigate particularly the effects introduced by
Nitsche's coupling, including the convergence performance and condition numbers
in statics as well as the extra "outlier" frequencies and corresponding
eigenmodes in structural dynamics. We present the Hertz test, the block test,
and a 3D self-contact example showing that the skew-symmetric Nitsche's
formulation is a suitable approach to simulate contact problems in IGA.
