6. Conclusions

In elasticity as in plasticity, whether for materials where \(\nu\) is equal to \(\mathrm{0,3}\) or \(\mathrm{0,5}\), the new element QUAS4 remains stable and the results always realistic, without any stress oscillations. This, as we have seen, is far from being the case for QUAD4. The stability of this new element in the face of test cases as severe as those presented in this report is comparable to that of the sub-integrated quadratic element QUAD8.

On the other hand, this element has the convergence of a linear element in terms of the number of degrees of freedom. It is therefore necessary to mesh with sufficient fineness to capture the stress gradients of the solution sought. This necessary refinement must be balanced against the time savings induced by under-integration.

On the examples treated, QUAS4 allowed a significant gain in calculation time of the order of 20% on average for elastic and elasto-plastic behavior laws. Note that these laws are relatively inexpensive to integrate. Much greater time savings are expected for laws that are more difficult to integrate.