Temporal stabilization nodal integration method for static and dynamic analyses of Reissner–Mindlin plates

Presenting a stabilized nodal integration method for analysis of Reissner-Mindlin plate.Squared-residual of equilibrium equations are considered in the potential energy functional.Giving an empirical value range of stabilization parameter through numerical tests.Numerical examples shown efficiency of the new method to improve calculation accuracy.The proposed scheme can eliminates the temporal instability successfully. In this paper, a temporal stabilized nodal integration method (sNIM) using 3-node triangular elements is formulated for elastic-static, free vibration and buckling analyses of Reissner-Mindlin plates. Two stabilization terms are added into the smoothed potential energy functional of the original nodal integration, consisting of squared-residual of equilibrium equations. A gradient smoothing technique (GST) is used to relax the continuity requirement of shape function. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are formed to perform the smoothing operation and the numerical integration. A stabilization parameter is finally introduced to the modified system for the sake of curing temporal instability. Numerical tests provide an empirical value range of stabilization parameter, within which very accurate and stable results can be obtained for both static and eigenvalue problems.