A nine-node displacement-based finite element for Reissner-Mindlin plates based on an improved formulation of the NIPE approach

The nodally integrated plate element formulation is an assumed strain finite element technique for shear deformable plates that enforce weakly the balance and the kinematic equations. The strain-displacement operators are derived via nodal integration satisfying a priori the kinematic weighted residual statement. The present work analyzes the NIPE technique, including the new element, by testing thoughtfully the sensitivity of the elements to severe geometry distortions. We propose an improvement that confers robustness to all element shapes developed by the NIPE formulation. We present also a new nine-node NIP element configuration. The new nine-node element uses bi-quadratic interpolations of the transverse displacement and rotations and is computed by means of a nine-node quadrature rule. A brief review of the improved triangular and quadrangular NIPEs is reported for elastic plate analyses. A few challenging benchmarks carried out on extreme distorted meshes illustrate the performance of the introduced NIP-Q9 element. We detail that the new NIPE formulation confers insensitivity to extreme distortions for the quadratic quadrilateral element and allows to solve for severe distortion with the NIPE family.