A 4-noded hybrid stress element with optimized stress for moderately thick and thin shallow shells

摘要

In this paper, a 4-noded hybrid stress finite element is developed for arbitrary plates and shallow shells. The finite element formulation is derived from the Hellinger-Reissner functional. In the process of the element derivation, the optimization principle of the numerical behaviour of multiple-variable FEM, in which an energy compatible condition is introduced to optimise the unconstrained stress trials, is employed. An appropriate unconstrained stress field is carefully chosen to validate the optimization. Because the transverse shear effect is taken into account, the element can be used for moderately thick and thin plates and shallow shells. Numerical study demonstrates that the present clement passes the patch test and is of high accuracy and free of superfluous zero energy deformation modes. There is no shear locking in the limit of thin plates and shells.