F. Laouafa et P. Royis, DISPLACEMENT FINITE-ELEMENT METHOD - NEW ALGEBRAIC STRUCTURE AND APPROPRIATE ALGORITHMS, Comptes rendus de l'Academie des sciences. Serie II. Mecanique, physique, chimie, astronomie, 325(6), 1997, pp. 347-352
In this note we state in a new form the algebraic problem arising from
the one-field displacement finite element method. The displacement ap
proach, in this discrete form, can be considered as the dual approach
(force or equilibrium) with subsidiary constraints. A more general uni
fication of both the one-field displacement finite element method and
the two-fields mired stress-displacement finite element method is prop
osed. Tt is based upon a discrete variational principle. We also demon
strate the numerical performances of this new approach.