| A general formulation for a family of N-node, higher-order, displacement-compatible, triangular, Reissner/Mindlin shear-deformable plate elements, MIN-N, is presented in this work. The development of MIN-N has been motivated primarily by the success of the 3-node, 9 degree-of-freedom, low-order, constant moment, anisoparametric triangular plate element, MIN3. This element avoids shear locking by using so-called anisoparametric interpolation, which is to use interpolation functions one degree higher for transverse displacement than for bending rotations. The methodology to derive members of the MIN-N family based on the anisoparametric strategy is presented. The family of MIN-N elements possesses complete, fully compatible kinematic fields. In the thin limit, the element must satisfy the Kirchhoff constraints of zero transverse shear strains. General formulas for these constraints are developed.; As an example of a higher-order member, the 6-node, 18 degree-of-freedom, triangular element MIN6 is developed. MIN6 has a cubic variation of transverse displacement and quadratic variation of rotational displacements. The element, with its straightforward, pure, displacement-based formulation, is implemented in a finite element program and tested extensively. Numerical results for both isotropic and orthotropic materials show that MIN6 exhibits good performance for both static and dynamic analyses in the linear, elastic regime. Explicit formulas for Kirchhoff constraints in the thin limit, in terms of element degrees-of-freedom, are developed. The results illustrate that the fully-integrated MIN6 element neither locks nor is excessively stiff in the thin limit, even for coarse meshes. |
