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Some continuous stress mixed formulations and inf-sup test

Berkovic M., Mijuca D., Grozdanović Ines

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 1

141-153

The most frequent motivation for the use of mixed methods is their robustness in the presence of certain limiting and extreme situations. At variance, the main goal of the present paper is to reconsider the use of mixed formulation as a tool for wider application, i.e., to study the stability of the proposed procedure treating problems in elasticity otherwise well suited for the solution by the usual displacement method. Computational procedure for the inf-sup test is outlined, and the results are given.

A direct clock sparse solution of the mixed finite element equations

Berković M., Drašković Z., Mijuca D.

Computer Assisted Mechanics and Engineering Sciences

1998

Vol. 5, nr 1

21-30

In this paper a practical procedure for the solution of really sized mixed problems, generating a continuous stress field (where appropriate) and having both the stress and displacement boundary conditions exactly satisfied, is described. The system matrix for the present formulation can be subdivided into the blocks, if the field variables (stresses and displacements) are separated for computational purposes. In addition, the structure of these blocks is sparse, similary as the structure of the stiffnes matrix in classical finite element analysis. Block sparse solution procedure, accounting for the pattern of the resulting system matrix is proposed. Computer implementation confirmed feasibility of the described solution procedure. In addition, numerical tests show remarkably high accuracy and convergence rate of the present mixed scheme for both the stresses and displacements. Due to high accuracy of the scheme, it can be competitive in comparaison with usual displacement approach, although the count of arethmetic operations for the same mesh density in mixed procedure can be order of magnitude larger than in classical finite element anaysis.