A theorem regarding the locking of tapered four‐noded membrane elements

Abstract It is shown that any four‐noded membrane element with two degrees of freedom per node will either lock in inplane bending or fail to pass a C 0 patch test when the element's shape is an isosceles trapezoid. This result effectively closes out further effort to extend the linear strain capability of such elements beyond what has already been achieved for rectangular and parallelogram shapes.