A triangular shear-flexible finite element for moderately thick laminated composite plates

Abstract An element of triangular shape is formulated by using independent descriptions of the total and flexural displacement components and strain energy written in terms of those components. Numerically exact integration is employed in the calculation of element stiffness matrix. The resulting finite element possesses eighteen degrees of freedom for the case of a symmetrically laminated plate. Numerical results are obtained for a wide range of meshes and thickness-to-span ratios, for isotropic, orthotropic and anisotropic plates, with different support and loading conditions. These are compared with available exact, series or finite element solutions. The derived element exhibits desirable convergence characteristics and validates the proposed approach for inclusion of transverse shear deformation.

[1]  A. K. Rao,et al.  Flexure of Thick Rectangular Plates , 1973 .

[2]  Ian M. Smith A finite element analysis for “moderately thick” rectangular plates in bending , 1968 .

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

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

[5]  S. Srinivas,et al.  Flexure of Simply Supported Thick Homogeneous and Laminated Rectangular Plates , 1969 .

[6]  S. A. Ambartsumyan,et al.  Theory of anisotropic shells , 1964 .

[7]  E. Reissner The effect of transverse shear deformation on the bending of elastic plates , 1945 .

[8]  J. Whitney,et al.  The Effect of Boundary Conditions on the Response of Laminated Composites , 1970 .

[9]  Lee R. Calcote,et al.  The analysis of laminated composite structures , 1969 .

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

[11]  Ahmed K. Noor,et al.  Shear-Flexible Finite-Element Models of Laminated Composite Plates and Shells. , 1975 .

[12]  Richard M. Barker,et al.  Three-dimensional finite-element analysis of laminated composites☆ , 1972 .

[13]  Numerical methods and refined plate theories , 1982 .

[14]  Vladimír Panc,et al.  Theories of elastic plates , 1975 .

[15]  O. C. Zienkiewicz,et al.  A refined higher-order C° plate bending element , 1982 .

[16]  R. Gallagher,et al.  An approach to the inclusion of transverse shear deformation in finite element plate bending analysis , 1984 .

[17]  P. K. Sinha,et al.  Transverse Bending of Cross-Ply Laminated Circular Cylindrical Plates , 1976 .

[18]  Tarun Kant,et al.  Numerical analysis of thick plates , 1982 .