Hybrid strain-based three-node flat triangular laminated composite shell elements

Abstract For large-scale linear and non-linear analysis of laminated composite shell structures, simple, accurate and efficient finite elements are critical to successes. In this paper, several simple three-node, six degrees of freedom (dof) per node, hybrid strain-based laminated composite flat triangular shell finite elements are presented. The stiffness matrices of these elements are obtained explicitly by using symbolic computer algebra packages, MAPLE and MACSYMA, and therefore, no numerical inversion of matrices and numerical integration are necessary during the derivation. The elements are compatible with the first-order shear deformation theory. A comprehensive study was performed on multi-layer plate and shell structures. Representative examples are presented to show that the elements have excellent performance in terms of convergence rate, accuracy, rank sufficient, no shear locking and efficiency. Results obtained indicate that the proposed simple shell elements can give very accurate answers for length to thickness ratios, μ ⩾ 20.

[1]  J. N. Reddy,et al.  THERMOELASTICITY OF CIRCULAR CYLINDRICAL SHELLS LAMINATED OF BIMODULUS COMPOSITE MATERIALS , 1981 .

[2]  A. Bhimaraddi,et al.  Dynamic response of orthotropic, homogeneous, and laminated cylindrical shells , 1985 .

[3]  Victor Birman,et al.  Parametric instability of thick, orthotropic, circular cylindrical shells , 1988 .

[4]  J. N. Reddy,et al.  A higher-order shear deformation theory of laminated elastic shells , 1985 .

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

[6]  M. Stein,et al.  Nonlinear theory for plates and shells including the effects of transverse shearing , 1986 .

[7]  Stanley B. Dong,et al.  On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation , 1972 .

[8]  Liviu Librescu,et al.  A shear deformable theory of laminated composite shallow shell-type panels and their response analysis II: Static response , 1989 .

[9]  Atef F. Saleeb,et al.  A mixed formulation of C0‐linear triangular plate/shell element—the role of edge shear constraints , 1988 .

[10]  John Argyris,et al.  A natural triangular layered element for bending analysis of isotropic, sandwich, laminated composite and hybrid plates , 1993 .

[11]  Ahmed K. Noor,et al.  A posteriori estimates for shear correction factors in multilayered composite cylinders , 1989 .

[12]  J. N. Reddy,et al.  Exact Solutions of Moderately Thick Laminated Shells , 1984 .

[13]  S. W. Lee,et al.  A nine-node assumed-strain finite element for composite plates and shells , 1987 .

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

[15]  D. Allman.  A compatible triangular element including vertex rotations for plane elasticity analysis , 1984 .

[16]  E. Reissner.  A note on variational principles in elasticity , 1965 .

[17]  J. D. Chieslar,et al.  A hybrid strain technique for finite element analysis of plates and shells , 1986 .

[18]  H. Norman Abramson,et al.  Applied mechanics surveys , 1966 .

[19]  Stanley B. Dong,et al.  On the Theory of Laminated Anisotropic Shells and Plates , 1962 .

[20]  Y. Stavsky,et al.  Vibrations of axially compressed laminated orthotropic cylindrical shells, including transverse shear deformation , 1980 .

[21]  T. Chow,et al.  On the Propagation of Flexural Waves in an Orthotropic Laminated Plate and Its Response to an Impulsive Load , 1971 .

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

[23]  A. Noor,et al.  Assessment of Computational Models for Multilayered Composite Shells , 1990 .

[24]  Charles W. Bert,et al.  Vibration of cylindrical shells of bimodulus composite materials , 1981 .

[25]  L. Penzes,et al.  Dynamic analysis of composite structures , 1977 .

[26]  C. W. S. To,et al.  Hybrid strain based three-node flat triangular shell elements , 1994 .

[27]  Ahmed K. Noor,et al.  Mechanics of anisotropic plates and shells - A new look at an old subject , 1992 .

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