Completely hierarchical p-version curved shell element for laminated composite plates and shells

This paper presents a new completely hierarchical three dimensional curved shell finite element formulation for linear static analysis of laminated composite plates and shells. The element displacement approximation can be of arbitrary polynomial orders pξ, pη and pξ in the ξ, η, and ξ directions thereby permitting strains of at least (pξ−1), (pη−1) and (pξ−1) order. The element approximation functions as well as the nodal variables are hierarchical. The element formulation ensures C0 continuity. The lamina properties are incorporated by numerically integrating the element stiffness matrix for each lamina. The formulation has no restriction on either the number of laminas or the layup pattern of the laminas. The geometry of the laminated shell element is described by the coordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node. The element formulation is equally effective for very thin as well as very thick laminated plates and curved shells. The results obtained from the present formulation are compared with those available in the literature as well as available analytical solutions.

[1]  R. B. Nelson,et al.  A Refined Theory for Laminated Orthotropic Plates , 1974 .

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

[3]  M. Levinson,et al.  An accurate, simple theory of the statics and dynamics of elastic plates , 1980 .

[4]  N. J. Pagano,et al.  Influence of Shear Coupling in Cylindrical. Bending of Anisotropic Laminates , 1970 .

[5]  S. T. Mau,et al.  A Refined Laminated Plate Theory , 1973 .

[6]  K. Sawamiphakdi,et al.  Large deformation analysis of laminated shells by ftnife element method , 1981 .

[7]  E. Reissner,et al.  On bending of elastic plates , 1947 .

[8]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[9]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[10]  A. W. Leissa,et al.  Analysis of Heterogeneous Anisotropic Plates , 1969 .

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

[12]  A. Rao,et al.  Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates , 1970 .

[13]  Raghu Natarajan,et al.  Finite element analysis of laminated composite plates , 1979 .

[14]  A. B. Basset.  On the Extension and Flexure of Cylindrical and Spherical Thin Elastic Shells , 1889 .

[15]  J. N. Reddy,et al.  A refined nonlinear theory of plates with transverse shear deformation , 1984 .

[16]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[17]  P. C. Chou,et al.  Elastic Constants of Layered Media , 1972 .

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

[19]  F. B. Hildebrand,et al.  Notes on the foundations of the theory of small displacements of orthotropic shells , 1949 .

[20]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

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

[22]  Barna A. Szabó,et al.  Hierarchic plate and shell models based on p-extension , 1988 .

[23]  Ivo Babuška,et al.  Accuracy estimates and adaptive refinements in finite element computations , 1986 .

[24]  Karan S. Surana,et al.  Curved shell elements based on hierarchical p‐approximation in the thickness direction for linear static analysis of laminated composites , 1990 .

[25]  K. Surana,et al.  Three dimensional curved shell finite elements for heat conduction , 1987 .

[26]  Karan S. Surana,et al.  Transition finite elements with temperature and temperature gradients as primary variables for axisymmetric heat conduction , 1986 .

[27]  N. J. Pagano,et al.  Elastic Behavior of Multilayered Bidirectional Composites , 1972 .

[28]  Curved Shell Element and Its Implementation in McAuto Strudl , 1979 .

[29]  E. Reissner,et al.  Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates , 1961 .

[30]  P. Basu,et al.  Analysis of singular cylindrical shells by p-version of FEM , 1989 .

[31]  K. Surana,et al.  Higher order hierarchical plates and curved shell elements based on p-approximation in the thickness direction , 1990 .

[32]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[33]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[34]  J. Whitney,et al.  The Effect of Transverse Shear Deformation on the Bending of Laminated Plates , 1969 .

[35]  R. Christensen,et al.  A High-Order Theory of Plate Deformation—Part 2: Laminated Plates , 1977 .

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

[37]  Karan S. Surana,et al.  Three dimensional solid-shell transition finite elements for heat conduction , 1987 .

[38]  K. Surana,et al.  Curved shell elements for elastostatics with p-version in the thickness direction , 1990 .

[39]  P. K. Basu,et al.  Some Trends in Computerized Stress Analysis , 1979 .