From deformation to mixed and hybrid formulation of the finite element method

Apostol Poceski

Theoretical and applied mechanics, Tome 5 (1979) no. 1, p. 135 .

Résumé

By applying the standard approach in the deformation method, mixed and hybrid methods can be developed. The proposed approach was applied to the problem of plate bending. Deformations in the element are expressed as functions of displacement and bending moment (9). Moments in a member should not be adopted completely independently, as was common in mixed and hybrid methods. Only bending moments can be adopted independently (10, 11), while torsional moments depend on bending moments (12, 13). With rough elements (with constant stresses for example), this is not the case, which is why such elements gave better results. A preliminary analysis with assumed deformations according to expression (9) shows that with the mixed method, a better accuracy of moments is obtained, while the accuracy of displacement is lower, but both quantities converge on one (upper) side, and their accuracy is of the same order. Such an assumption of deformations allows the direct effect of the divided load to be taken into account. In this case, the number of unknowns per node does not increase, but can be smaller. A general functional given by expressions (25) and (32) was developed, from which all the variational principles applied in the finite element method can be derived.