Behaviour of plate elements based on the first‐order shear deformation theory

Abstract

A study of the behaviour of shear deformable plate finite elements is carried out to determine why and under what conditions these elements lock, or become overly stiff. A new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side‐to‐thickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and are interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various plate elements. These include bilinear, biquadratic, eight‐node serendipity and heterosis elements. These analytical findings are compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behaviour of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration.