A three-dimensional layer-wise constant shear element for general anisotropic shell-type structures

This paper deals with the development of a new three-dimensional element with two-dimensional kinematic constraints capable of analysing the mechanical behaviour of the laminated anisotropic shell-type structures. This element, originally developed for the linear analysis of plates, is extended for the linear analysis of laminated composite shells. The element can represent arbitrarily curved shells with variable number of layers and thicknesses, including ply drop-off problems. The element was validated in a previous work by the patch test. All the analytical details necessary to make possible the shell analysis are presented here. Examples are reported to show the capability of the element to predict the behaviour of complex structures and a refined computation of the stresses is carried out by integrating the equilibrium equations.

[1]  Anthony N. Palazotto,et al.  Nonlinear finite element analysis of thick composite plates using cubic spline functions , 1985 .

[2]  Reaz A. Chaudhuri,et al.  An equilibrium method for prediction of transverse shear stresses in a thick laminated plate , 1986 .

[3]  J. N. Reddy,et al.  General two-dimensional theory of laminated cylindrical shells , 1990 .

[4]  K. Chandrashekhara,et al.  Geometrically non-linear transient analysis of laminated, doubly curved shells , 1985 .

[5]  E. Barbero,et al.  On a generalized laminate theory with application to bending, vibration, and delamination buckling in composite laminates , 1989 .

[6]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

[7]  Paul Seide,et al.  An improved approximate theory for the bending of laminated plates , 1980 .

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

[9]  Ever J. Barbero,et al.  A 3-D finite element for laminated composites with 2-D kinematic constraints , 1992 .

[10]  J. N. Reddy,et al.  A plate bending element based on a generalized laminate plate theory , 1988 .

[11]  Marcelo Epstein,et al.  Nonlinear analysis of multilayered shells , 1977 .

[12]  J. N. Reddy,et al.  On the Generalization of Displacement-Based Laminate Theories , 1989 .

[13]  Hidenori Murakami,et al.  Laminated Composite Plate Theory With Improved In-Plane Responses , 1986 .

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

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

[16]  David R. Owen,et al.  A refined analysis of laminated plates by finite element displacement methods—I. Fundamentals and static analysis , 1987 .

[17]  S. Srinivas,et al.  A refined analysis of composite laminates , 1973 .

[18]  J. N. Reddy,et al.  An accurate determination of stresses in thick laminates using a generalized plate theory , 1990 .

[19]  Marcelo Epstein,et al.  A finite element formulation for multilayered and thick plates , 1983 .

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

[21]  N. Pagano,et al.  Exact Solutions for Composite Laminates in Cylindrical Bending , 1969 .

[22]  Raffaele Zinno,et al.  Nonlinear analysis of doubly curved composite shells of bimodular material , 1993 .

[23]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

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

[25]  Ever J. Barbero 3-D finite element modeling of laminated composites by layer-wise constant shear elements , 1991 .