ABSTRACT
Some mechanical problems involve non-symmetric constitutive relations. In concrete, soil or rocks mechanics the non-associativity of the flow rule leads when used within a finite element analysis, to a global non-symmetric and non-linear algebraic problem. The iterative algorithm GMRES (Generalized Minimal RESidual) is advocate for solving such non-symmetric problems. The original methods presented in this paper show that the algebraic systems coming from finite element analyses based on the classical displacement one-field approach can be solved without computing any stiffness matrix. The displacement one field algebraic problem can be stated in a mixed like form closer to the GMRES algorithm, and moreover closer to the mechanical problem. This new form of the problem leads to inexpensive improvements of FEM computations. The performances of the method increase greatly in the non-linear case, in three dimensional analyses and when reduced integration is carried out.
