We formulate a cut finite element method for linear elasticity based on
higher order elements on a fixed background mesh. Key to the method is a
stabilization term which provides control of the jumps in the derivatives of
the finite element functions across faces in the vicinity of the boundary. We
then develop the basic theoretical results including error estimates and
estimates of the condition number of the mass and stiffness matrices. We apply
the method to the standard displacement problem, the frequency response
problem, and the eigenvalue problem. We present several numerical examples
including studies of thin bending dominated structures relevant for engineering
applications. Finally, we develop a cut finite element method for fibre
reinforced materials where the fibres are modeled as a superposition of a truss
and a Euler-Bernoulli beam. The beam model leads to a fourth order problem
which we discretize using the restriction of the bulk finite element space to
the fibre together with a continuous/discontinuous finite element formulation.
Here the bulk material stabilizes the problem and it is not necessary to add
additional stabilization terms
