A C° continuous linear beam/bilinear plate flexure element

Abstract

Design of a simple C°-continuous beam/plate flexure element based on a shear-deformable theory is attempted. Emphasis is placed on development of a low order linear/bilinear element. However, past experience shows that such elements become very "stiff"especially when thickness is reduced (conforming to Kirchhoff mode). This phenomenon is called "locking."Attempts have been made in the last several years by a few investigators to overcome this problem. The locking problem is resolved here through a new approach. The total strain energy is split into bending and shear energies and an antiparameter in the shear energy term is introduced to avoid locking. By numerical experimentation on beam and plate problems it is shown that the present approach gives good results in the thin limit. It is also shown that the additional/spurious zero energy modes do not arise here because reduced/selective integration is avoided.