Mindlin plate analysis by segmentation method

A method for the numerical analysis of rectangular plates based on Mindlin's theory is presented. Any two opposite edges are assumed to be simply supported in the present analysis. A variety of boundary conditions including the mixed and the nonhomogeneous types can be specified along either of the remaining two opposite edges. Numerical results are presented for four examples. The present results clearly show the discrepancies in the results of the usual thin plate theory. Some of the problems associated with the use of the thin plate theory based on Kirchhoff's assumptions are clarified. Finally it is shown that the present segmentation method which is based on the numerical integration of the governing equation system is efficient, economical, reliable, and very accurate in such applications.

[1]  Tarun Kant,et al.  Numerical integration of linear boundary value problems in solid mechanics by segmentation method , 1981 .

[2]  J. Altenbach.  Zienkiewicz, O. C., The Finite Element Method. 3. Edition. London. McGraw‐Hill Book Company (UK) Limited. 1977. XV, 787 S. , 1980 .

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

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

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

[6]  R. Christensen,et al.  A HIGH-ORDER THEORY OF PLATE DEFORMATION, PART 1: HOMOGENEOUS PLATES , 1977 .

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

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

[9]  Y. K. Cheung,et al.  FINITE STRIP METHOD IN STRUCTURAL ANALYSIS , 1976 .

[10]  E. Reissner,et al.  On transverse bending of plates, including the effect of transverse shear deformation☆ , 1975 .

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

[12]  R. Archer,et al.  Numerical Solution of Moderately Thick Plates , 1974 .

[13]  J. Stephenson,et al.  Analysis of Noncircular Cylindrical Shells , 1973 .

[14]  Sir O Williams.  SIR (EVAN) OWEN WILLIAMS, KBE. (1890-1969). , 1969 .

[15]  H. Langhaar,et al.  Transverse Shearing Stress in Rectangular Plates , 1968 .

[16]  A. L. Gol'denveizer.  Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity , 1962 .

[17]  V. L. Salerno,et al.  Effect of Shear Deformations on the Bending of Rectangular Plates , 1960 .

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

[19]  L. Kantorovich,et al.  Approximate methods of higher analysis , 1960 .

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

[21]  E. Reissner.  On a Variational Theorem in Elasticity , 1950 .

[22]  A. Green.  On Reissner’s theory of bending of elastic plates , 1949 .

[23]  E. Reissner.  ON THE THEORY OF BENDING OF ELASTIC PLATES , 1944 .