A comparison of lagrangian and serendipity mindlin plate elements for free vibration analysis

Abstract The performance of five Lagrangian and Serendipity (4,8,9,12 and 16 noded) isoparametric elements in the free vibration finite analysis of Mindlin plates is evaluated. The results are compared with well established analytical and numerical solutions based on Mindlin's thick plate theory and three dimensional elasticity solutions.

[1]  E. Hinton,et al.  Reduced integration, function smoothing and non-conformity in finite element analysis (with special reference to thick plates) , 1976 .

[2]  Bruce M. Irons,et al.  Shape function subroutine for an isoparametric thin plate element , 1973 .

[3]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[4]  E. Hinton,et al.  A finite element method for the free vibration of plates allowing for transverse shear deformation , 1976 .

[5]  G. C. Wright,et al.  An economical method for determining the smallest eigenvalues of large linear systems , 1971 .

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

[7]  E. Citipitioglu,et al.  A general isoparametric finite element program SDRC SUPERB , 1977 .

[8]  E. Hinton,et al.  A study of quadrilateral plate bending elements with ‘reduced’ integration , 1978 .

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

[10]  A. Rao,et al.  Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates , 1970 .

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

[12]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[13]  Isaac Fried,et al.  Finite element mass matrix lumping by numerical integration with no convergence rate loss , 1975 .

[14]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[15]  Raymond D. Mindlin,et al.  FLEXURAL VIBRATIONS OF RECTANGULAR PLATES , 1955 .

[16]  E. Brunelle,et al.  Initially Stressed Mindlin Plates , 1974 .

[17]  Bruce M. Irons,et al.  EXPERIENCE WITH THE PATCH TEST FOR CONVERGENCE OF FINITE ELEMENTS , 1972 .

[18]  Ray W. Clough,et al.  Improved numerical integration of thick shell finite elements , 1971 .

[19]  E. Hinton,et al.  A thick finite strip solution for static, free vibration and stability problems , 1976 .

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

[21]  H. Reismann,et al.  Dynamics of Initially Stressed Plates , 1976 .

[22]  E. Hinton,et al.  A SIMPLE FINITE ELEMENT SOLUTION FOR PLATES OF HOMOGENOUS, SANDWICH AND CELLULAR CONSTRUCTION. , 1975 .

[23]  Martin Cohen,et al.  The “heterosis” finite element for plate bending , 1978 .

[24]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .