A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates

A comprehensive analysis of available models and techniques to evaluate transverse shear and normal stresses in multilayered orthotropic plates is given in this paper. Transverse stresses evaluated a posteriori by integration of the 3D indefinite equilibrium equations and from Hooke's law are compared to those given a priori by an assumed stress model (if implemented). Classical theories formulated on the basis of assumed through-the-thickness displacement fields as well as mixed modelings originated by a Reissner's mixed variational theorem are considered. Both cases of Equivalent Single Layer Models (ESLMs) and Layer Wise Models (LWMs) have been investigated. Linear up to fourth N-order expansions, in the thickness layer/plate direction, have been implemented for the introduced displacement and stress fields. As a result, theories describing so-called zigzag effects and accounting for interlaminar continuous transverse stresses are compared to simplified cases which neglect zigzag and violate interlaminar equilibrium. A numerical investigation has been restricted to bending of simply supported, orthotropic plates. It is mainly concluded that: (1) N-order increasing, layer-wise analysis could furnish excellent a priori as well as a posteriori description of transverse stresses of laminate thick and thin plates; ESLM accuracy remains subordinate to laminate lay-out, to plate thickness and to two-dimensional modelings (mixed results are much more accurate than classical ones). (2) The discrepancy among the three manners of evaluating transverse shear stresses is scarcely dependent on plate thickness ratio. (3) In most of the considered cases, the best description of transverse stresses has been obtained by layer-wise mixed analysis upon integration of the 3D indefinite equilibrium equations.

[1]  Erasmo Carrera,et al.  CZ° requirements—models for the two dimensional analysis of multilayered structures , 1997 .

[2]  Paolo Gaudenzi,et al.  A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates , 1995 .

[3]  E. Carrera.  Layer-Wise Mixed Models for Accurate Vibrations Analysis of Multilayered Plates , 1998 .

[4]  C. Sun,et al.  Theories for the Dynamic Response of Laminated Plates , 1973 .

[5]  Mohamed Samir Hefzy,et al.  Review of Knee Models , 1988 .

[6]  Hidenori Murakami,et al.  A Composite Plate Theory for Arbitrary Laminate Configurations. , 1987 .

[7]  E. Reissner.  On a mixed variational theorem and on shear deformable plate theory , 1986 .

[8]  Erasmo Carrera.  Single- vs Multilayer Plate Modelings on the Basis of Reissner's Mixed Theorem , 2000 .

[9]  Hidenori Murakami,et al.  A high-order laminated plate theory with improved in-plane responses☆ , 1987 .

[10]  Erasmo Carrera,et al.  Mixed layer-wise models for multilayered plates analysis , 1998 .

[11]  J. N. Reddy,et al.  Modelling of thick composites using a layerwise laminate theory , 1993 .

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

[13]  Erasmo Carrera,et al.  Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis , 1998 .

[14]  E. Reissner,et al.  Reflections on the Theory of Elastic Plates , 1985 .

[15]  M. Di Sciuva,et al.  A general quadrilateral multilayered plate element with continuous interlaminar stresses , 1993 .

[16]  Erasmo Carrera,et al.  Transverse Normal Stress Effects in Multilayered Plates , 1999 .

[17]  E. Reissner.  On a certain mixed variational theorem and a proposed application , 1984 .

[18]  Ahmed K. Noor,et al.  Assessment of Shear Deformation Theories for Multilayered Composite Plates , 1989 .

[19]  Moussa Karama,et al.  Comparison of various laminated plate theories , 1997 .

[20]  Rakesh K. Kapania,et al.  Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling. , 1989 .

[21]  Maenghyo Cho,et al.  Efficient higher order composite plate theory for general lamination configurations , 1993 .

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

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

[24]  Dewey H. Hodges,et al.  Application of the variational-asymptotical method to laminated composite plates , 1993 .

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

[26]  Ahmed K. Noor,et al.  Stress and free vibration analyses of multilayered composite plates , 1989 .

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

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

[29]  T. K. Varadan,et al.  Refinement of higher-order laminated plate theories , 1989 .

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

[31]  Teh-Min Hsu,et al.  A theory of laminated cylindrical shells consisting of layers of orthotropic laminae , 1970 .

[32]  Dewey H. Hodges,et al.  On asymptotically correct linear laminated plate theory , 1996 .

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

[34]  J. Ren,et al.  A new theory of laminated plate , 1986 .