When standard conforming elements are used for problems involving nearly incompressible materials, the locking phenomenon(Poisson locking) will become increasingly apparent as the Poisson's ratio approaches the value of 0.5.
In this thesis, using the shape functions with high degrees Legendre polynomials, Poisson locking phenomenon does not occur in the incompressible materials. In the solution of the p-version of the finite element method, the rate of convergence is not influenced by different Poisson's ratio in a straight domain. But problems involving a curved boundary are not the case.
Therefore it is necessary to add the incompressible constraint to the p-version of the finite element program by the mixed formulation. The geometric mapping of arbitrary curved boundary is exactly achieved by the transfinite mapping. Two examples about the cantilever beam and plate with the rigid hall are presented.
