An accurate shear‐deformable six‐node triangular plate element for laminated composite structures

A six-node triangle plate/shell element is developed for the analysis of laminated composite structures. This model is formulated using Hamilton's principle along with a first-order (Reissner/Mindlin) shear deformation theory. The element is based upon an isoparametric representation along with an interdependent interpolation strategy; bicubic polynomials for the transverse displacement and biquadratic polynomials for the element geometry, in-plane displacements and rotations. The resulting element, which is evaluated using exact numerical integration, has correct rank and is free of shear ‘locking’. Numerical results are presented that validate the new element and prove its outstanding convergence capabilities in comparison to existing triangular elements using standardized test problems (elastic eigenvalue analysis, patch test, static simply supported square-plate solutions) and experimentally measured vibration data of cantilevered isotropic and composite plates.

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

[2]  G. R. Cowper,et al.  Gaussian quadrature formulas for triangles , 1973 .

[3]  H. V. Lakshminarayana,et al.  A shear‐flexible triangular finite element model for laminated composite plates , 1984 .

[4]  Jean-Louis Batoz,et al.  An explicit formulation for an efficient triangular plate‐bending element , 1982 .

[5]  J. B. Kosmatka,et al.  The Use of System Identification to Refine Structural Dynamic Models , 1991 .

[6]  Fuh-Gwo Yuan,et al.  A cubic triangular finite element for flat plates with shear , 1989 .

[7]  S. V. Kulkarni,et al.  Shear Correction Factors for Laminated Plates , 1979 .

[8]  T. Hughes,et al.  A three-node mindlin plate element with improved transverse shear , 1985 .

[9]  Stanley B. Dong,et al.  Shear Constitutive Relations for Laminated Anisotropic Shells and Plates: Part I—Methodology , 1992 .

[10]  G. Dhatt,et al.  A new triangular discrete Kirchhoff plate/shell element , 1986 .

[11]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

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

[13]  A. Pifko,et al.  Aspects of a simple triangular plate bending finite element , 1980 .

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

[15]  S. B. Dong,et al.  On a hierarchy of conforming timoshenko beam elements , 1981 .

[16]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[17]  E. Kosko,et al.  Static and dynamic applications of a high- precision triangular plate bending element , 1969 .

[18]  J. Whitney,et al.  Shear Correction Factors for Orthotropic Laminates Under Static Load , 1973 .