Computerized generalized displacement method for finite element analysis of incompressible material

Abstract

A new approach to deal with the finite element analysis of incompressible material is presented. The constrained variational problem relating to the analysis of incompressible material is transformed into two unconstrained variational problems in two corresponding displacement subspaces, which are called the incompressible‐deviatoric (Sd) and the compressible‐undeviatoric (Sc) displacement subspaces respectively. The displacement and deviatoric stress, and the pressure fields, are determined by means of variations in the two subspaces respectively. As compared with some current methods, it is found that the present method is capable of solving the problem of incompressible material with v = 0.5, and that there is no problem about the existence of solution. Further, the ill‐conditioning of the global matrix can be entirely eliminated and the computational effort can be considerably reduced as well. The formulation for the finite element analysis of incompressible material with material or geometrical non‐linearity based on the subspace Sd are given in the paper. The numerical results for some examples show the advantages of the approach presented in the paper.

Citation

Xi‐Kui, L. (1984), "Computerized generalized displacement method for finite element analysis of incompressible material", Engineering Computations, Vol. 1 No. 4, pp. 336-342. https://doi.org/10.1108/eb023589