Optimization of stress modes by energy compatibility for 4-node hybrid quadrilaterals

Optimal hybrid stress quadrilaterals can be obtained by adopting appropriate stresses and displacements, and satisfying the energy compatibility condition is shown to be an ultimate key to obtaining optimal stress modes. By using compatible isoparametric bilinear (Q4) displacements and 5-parameter energy compatible stresses of the combined hybrid nite element CH(0-1), a robust 4-node plane stress element ECQ4 is derived. Equivalence to another hybrid stress element LQ6 with 9-parameter complete linear stresses based on a modi ed Hellinger–Reissner principle is established. A convergence analysis is given and numerical experiments show that elements ECQ4 \LQ6 have high performance, i.e. are accurate at coarse meshes, insensitive to mesh distortions and free from locking