On the behavior of shear deformable plate elements

Abstract

An investigation of the behavior of shear deformable plate finite elements is conducted to determine why and under what conditions these elements lock, or become overly stiff. For this purpose, a new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side-tothickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and they are easily interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. Moreover, the technique is applicable to any displacement-based shear deformable beam, plate or shell element regardless of the shear deformation theory or the order of the Gauss-Legendre integration rule which is used to numerically evaluate the stiffness coefficients. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various Mindlin and Reddy-type beam and plate elements. These analytical findings are then compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behavior 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.