A Gradient Stable Node-Based Smoothed Discrete Shear Gap Method for Analysis of Reissner–Mindlin Plates

Yadong Xu,Jinsong Tang,Guangsong Chen

doi:10.1155/2020/8881983

Yadong Xu, Jinsong Tang + Show 1 more

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https://doi.org/10.1155/2020/8881983

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Abstract

In this paper, a gradient stable node-based smoothed discrete shear gap method (GS-DSG) using 3-node triangular elements is presented for Reissner–Mindlin plates in elastic-static, free vibration, and buckling analyses fields. By applying the smoothed Galerkin weak form, the discretized system equations are obtained. In order to carry out the smoothing operation and numerical integration, the smoothing domain associated with each node is defined. The modified smoothed strain with gradient information is derived from the Hu–Washizu three-field variational principle, resulting in the stabilization terms in the system equations. The stabilized discrete shear gap method is also applied to avoid transverse shear-locking problem. Several numerical examples are provided to illustrate the accuracy and effectiveness. The results demonstrate that the presented method is free of shear locking and can overcome the temporal instability issues, simultaneously obtaining excellent solutions.

Highlights

Theoretical FormulationsSubstituting equations (22)–(24) into (6), a set of discretized algebraic system equations of Reissner–Mindlin plates for static analysis can be obtained in the following matrix form: Kd􏽢 − 􏽢f 0,
[59], wherein the nodal integration technique is directly applied to obtain stable solutions
In order to overcome the temporal instability problem encountered in the nodal integration process, the smoothed Galerkin weak form is applied by using the strain smoothing technique with gradient information, which is derived from the Hu–Washizu three-field variation principle. e stabilized discrete shear gap method is incorporated into the presented method to avoid the transverse shear locking and improve the accuracy of the present formulation. e numerical examples presented demonstrate that the present method is both free of shear locking and temporal instability

Summary

Theoretical Formulations

Substituting equations (22)–(24) into (6), a set of discretized algebraic system equations of Reissner–Mindlin plates for static analysis can be obtained in the following matrix form: Kd􏽢 − 􏽢f 0,. 3. The Formulation of Gradient Stable NodeBased Smoothed Integration and Discrete Shear Gap Technique. The structural stiffness matrix is composed of three parts, namely, Km, Kb, and Ks. On the one hand, for Km and Kb, we take the method of gradient stable node-based smoothed integration to avoid temporal instability and spatial instability; for Ks, on the other hand, the discrete shear gap technique is employed to avoid the shear-locking problem. We can discretize the problem domain Ω with Ne triangular elements as in standard FEM, but the integral required in this work is based on the node and utilizes strain smoothing operations.

Numerical Examples

Static Analysis

10 Figure 11

18 Modes 1 2 3 4 5 6 7 8 9 10 11 12

Findings

Conclusions