A new locking-free equilibrium mixed element for plane elasticity with continuous displacement interpolation

摘要

With reference to plane elastic problems, we first show that using the Johnson and Mercier (JM) element [C. Johnson, B. Mericer, Numer. Math. 30 (1978) 103] for the stresses and an H~1 piecewise linear interpolation for the displacements leads to a severe locking when the Lame coefficient λ tends to infinity, i.e. in the case of an incompressible material. Motivated by the need to have a continuous displacement field that emerges in several engineering applica- tions, we use an eigenvalue argument to prove that locking is due to the presence of the (element-average) pressure among the degrees of freedom.