In the assumed displacement,
or primal, hybrid finite element method, the requirements of continuity
of displacements across the sides are regarded as constraints, imposed
using Lagrange multipliers. In this paper, such a formulation for linear
elasticity, in which the polynomial approximation functions are not associated
with nodes, is presented. Elements with any number of sides may be easily
used to create meshes with irregular vertices, when performing a non-uniform
h-refinement.
Meshes of non-uniform degree may be easily created, when performing an
hp-refinement.
The occurrence of spurious static modes in meshes of triangular elements,
when compatibility is strongly enforced, is discussed. An algorithm for
the automatic selection, based on the topology of a mesh of triangular
elements, of the sides in which to decrease the degree of the approximation
functions, in order to eliminate all these spurious modes and preserve
compatibility, is presented. A similar discussion is presented for the
occurrence of spurious static modes in meshes of tetrahedral elements.
An algorithm, based on heuristic criteria, that succeeded in eliminating
these spurious modes and preserving compatibility in all the meshes of
tetrahedral elements of uniform degree that were tested, is also presented.
KEY WORDS: assumed displacement
hybrid finite element method; primal hybrid finite element method; Lagrange
multipliers; spurious static modes; linear elasticity; conforming elements.