论文信息 - A stabilization matrix for the bilinear mindlin plate element

A stabilization matrix for the bilinear mindlin plate element

Abstract The reduced integration of the four node quadrilateral plate element based on Mindlin theory results in zero energy modes other than the rigid body modes. These modes present difficulties in certain situations. In this paper we suggest a method to remove these zero-energy (kinematic) modes by perturbing the stiffness by a stabilization matrix. This approach eliminates the element's kinematic modes without inducing locking and thus does not affect its convergence.

[1] E. Hinton,et al. Transient and pseudo‐transient analysis of Mindlin plates , 1980 .

[2] T. Hughes,et al. Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element , 1981 .

[3] Medhat A. Haroun,et al. Reduced and selective integration techniques in the finite element analysis of plates , 1978 .

[4] Robert D. Cook,et al. More on reduced integration and isoparametric elements , 1972 .

[5] G. A. Frazier,et al. Treatment of hourglass patterns in low order finite element codes , 1978 .

[6] Arthur W. Leissa,et al. Vibration of Plates , 2021, Solid Acoustic Waves and Vibration.

[7] Thomas J. R. Hughes,et al. A simple and efficient finite element for plate bending , 1977 .

[8] T. Belytschko,et al. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control , 1981 .

[9] E. Hinton,et al. A comparison of lagrangian and serendipity mindlin plate elements for free vibration analysis , 1979 .

[10] S. Timoshenko,et al. THEORY OF PLATES AND SHELLS , 1959 .

[11] S. L. Lee,et al. Uniformly loaded rectangular plate supported at the corners , 1960 .