Mixed formulation finite elements for mindlin theory plate bending

Two new finite elements are developed for the Mindlin theory plate bending problem. The formulation is based on the modified Hellinger-Reissner principle with independent transverse shear strains. Numerical examples indicate that, with properly assumed transverse shear strains, these new elements designated as PLAT8 and PLAT8H do not exhibit locking effect even for very thin plates.

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

[2]  Theodore H. H. Pian,et al.  Basis of finite element methods for solid continua , 1969 .

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

[4]  Richard H. Macneal,et al.  A simple quadrilateral shell element , 1978 .

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

[6]  Klaus-Jürgen Bathe,et al.  A study of three‐node triangular plate bending elements , 1980 .

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

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

[9]  Robert L. Spilker,et al.  The hybrid‐stress model for thin plates , 1980 .

[10]  Pin Tong,et al.  New displacement hybrid finite element models for solid continua , 1970 .

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

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

[13]  Kaspar Willam,et al.  Some considerations for the evaluation of finite element models , 1974 .

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

[15]  J. Z. Zhu,et al.  The finite element method , 1977 .

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