Finite element free vibration analysis of eccentrically stiffened plates

A new finite element model is proposed for free vibration analysis of eccentrically stiffened plates. The formulation allows the placement of any number of arbitrarily oriented stiffeners within a plate element without disturbing their individual properties. A plate-bending element consistent with the Reissner-Mindlin thick plate theory is employed to model the behaviour of the plating. A stiffener element, consistent with the plate element, is introduced to model the contributions of the stiffeners. The applied plate-bending and stiffener elements are based on mixed interpolation of tensorial components (MITC), to avoid spurious shear locking and to guarantee good convergence behaviour. Several numerical examples using both uniform and distorted meshes are given to demonstrate the excellent predictive capability of this approach.

[1]  D. Arnold.  Discretization by finite elements of a model parameter dependent problem , 1981 .

[2]  C. F. Kollbrunner,et al.  Torsion in Structures , 1970 .

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

[4]  M. Mukhopadhyay,et al.  Finite element free vibration of eccentrically stiffened plates , 1988 .

[5]  Abhijit Mukherjee,et al.  Finite element free vibration analysis of stiffened plates , 1986, The Aeronautical Journal (1968).

[6]  M. Mukhopadhyay,et al.  A review of dynamic behavior of stiffened plates , 1986 .

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

[8]  E. Hinton,et al.  A family of quadrilateral Mindlin plate elements with substitute shear strain fields , 1986 .

[9]  Eugenio Oñate,et al.  A general methodology for deriving shear constrained Reissner‐Mindlin plate elements , 1992 .

[10]  J. B. Caldwell,et al.  An isoparametric eccentrically stiffened plate bending element , 1988 .

[11]  C. R. Hazell,et al.  Vibration studies on some integral rib-stiffened plates , 1977 .

[12]  K. Bathe,et al.  The MITC7 and MITC9 Plate bending elements , 1989 .

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

[14]  Ian Smith.  The finite element method, 3rd edn, O. C. Zienkiewicz, McGraw‐Hill (U.K.) Ltd. 1977. No. of pages 787 , 1978 .

[15]  S K Satsangi,et al.  ISOPARAMETRIC STIFFENED PLATE BENDING ELEMENT FOR THE ANALYSIS OF SHIPS' STRUCTURES , 1984 .

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

[17]  M. Mukhopadhyay,et al.  Literature Review : Recent Advances On the Dynamic Behavior of Stiffened Plates , 1989 .

[18]  N. E. Shanmugam,et al.  Free vibration of plated structures by grillage method , 1985 .

[19]  P. S. Nair,et al.  On vibration of plates with varying stiffener length , 1984 .

[20]  A. Deb,et al.  Finite element models for stiffened plates under transverse loading , 1988 .

[21]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .