Non-linear theory of laminated shells accounting for continuity conditions of displacements and tractions at layer interfaces

Abstract The present paper is devoted to the formulation of the theory of laminated anisotropic shells. Firstly, a unified representation of displacement variation across the thickness of arbitrary shaped laminated shells is derived on the basis of rigorous kinematical analysis, and then a Karman-type non-linear theory of such shells is established after taking some approximations for the displacement variation. The theory satisfies the continuity conditions of displacements and tractions at layer interfaces as well as the external boundary conditions on the bounding surfaces, and the governing equations contain only five independent variables. In order to assess the accuracy of the theory, numerical results for some special cases are illustrated and compared with the corresponding exact solutions of three-dimensional elasticity.

[1]  T. K. Varadan,et al.  ACCURATE BENDING ANALYSIS OF LAMINATED ORTHOTROPIC PLATES , 1990 .

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

[3]  Marco Di Sciuva,et al.  Multilayered anisotropic plate models with continuous interlaminar stresses , 1992 .

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

[5]  Maenghyo Cho,et al.  An efficient higher-order plate theory for laminated composites , 1992 .

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

[7]  J. Whitney,et al.  A Refined Theory for Laminated Anisotropic, Cylindrical Shells , 1974 .

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

[9]  Maurice Touratier,et al.  A refined theory of laminated shallow shells , 1992 .

[10]  L. Doxsee.  A higher-order theory of hygrothermal behavior of laminated composite shells , 1989 .

[11]  Liviu Librescu,et al.  Substantiation of a shear-deformable theory of anisotropic composite laminated shells accounting for the interlaminae continuity conditions , 1991 .

[12]  J. Ren,et al.  Exact solutions for laminated cylindrical shells in cylindrical bending , 1987 .

[13]  Liviu Librescu,et al.  Refined geometrically nonlinear theories of anisotropic laminated shells , 1987 .

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

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

[16]  Liviu Librescu,et al.  Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures , 1975 .

[17]  Linghui He,et al.  A linear theory of laminated shells accounting for continuity of displacements and transverse shear stresses at layer interfaces , 1994 .

[18]  Jack R. Vinson,et al.  Laminated Transversely Isotropic Cylindrical Shells , 1971 .

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

[20]  J. N. Reddy,et al.  On a moderate rotation theory of laminated anisotropic shells—Part 1. Theory☆ , 1990 .

[21]  M. Di Sciuva,et al.  An Improved Shear-Deformation Theory for Moderately Thick Multilayered Anisotropic Shells and Plates , 1987 .

[22]  T. K. Varadan,et al.  Large deflection analysis of laminated composite plates , 1993 .