A comparison of zigzag functions for the bending, vibration and buckling analysis of multilayered composite and sandwich plates

In the framework of the Zigzag theories, an important role is played by the zigzag function. In the open literature, two kind of zigzag functions exist. A comparison of the advantages in adopting one zigzag function rather than the other is compulsory. In this work, with a general formalism, a displacement-based model wherein the First Order Shear Deformation (FSDT) kinematic is enriched by adding a zigzag contribution only to the inplane displacements description, is developed. By selecting the zigzag function, two models arise from the general formulation. Comparison on the response predictive capabilities ensured by the two zigzag functions, is made. Results pertaining the elastostatic deformation, free vibrations and buckling load problems of square sandwich plates subjected to several load and boundary conditions are compared with exact Elasticity solutions, when available, or high-fidelity FE model

[1]  Marco Gherlone,et al.  Assessment of the Refined Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different theories , 2013 .

[2]  Marco Di Sciuva,et al.  Development of an anisotropic, multilayered, shear-deformable rectangular plate element , 1985 .

[3]  Santosh Kapuria,et al.  Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory , 2008 .

[4]  M. Ganapathi,et al.  FREE VIBRATION ANALYSIS OF MULTI-LAYERED COMPOSITE LAMINATES BASED ON AN ACCURATE HIGHER-ORDER THEORY , 2001 .

[5]  Erasmo Carrera,et al.  Improved Response of Unsymmetrically Laminated Sandwich Plates by Using Zig-zag Functions , 2009 .

[6]  P. Vidal,et al.  A sine finite element using a zig-zag function for the analysis of laminated composite beams , 2011 .

[7]  Ronald C. Averill,et al.  Static and dynamic response of moderately thick laminated beams with damage , 1994 .

[8]  Ahmed K. Noor,et al.  Three‐Dimensional Solutions for Initially Stressed Structural Sandwiches , 1994 .

[9]  R. P. Shimpi,et al.  A Review of Refined Shear Deformation Theories for Isotropic and Anisotropic Laminated Beams , 2001 .

[10]  Santosh Kapuria,et al.  Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams , 2004 .

[11]  M. D. Sciuva,et al.  BENDING, VIBRATION AND BUCKLING OF SIMPLY SUPPORTED THICK MULTILAYERED ORTHOTROPIC PLATES: AN EVALUATION OF A NEW DISPLACEMENT MODEL , 1986 .

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

[13]  Philippe Vidal,et al.  A thermomechanical finite element for the analysis of rectangular laminated beams , 2006 .

[14]  K. Bhaskar,et al.  Analytical solutions for flexure of clamped rectangular cross-ply plates using an accurate zig–zag type higher-order theory , 2006 .

[15]  E. Carrera Historical review of Zig-Zag theories for multilayered plates and shells , 2003 .

[16]  Marco Gherlone,et al.  A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics , 2010 .

[17]  Ugo Icardi,et al.  Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations , 2001 .

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

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

[20]  Marco Gherlone,et al.  A Refined Zigzag Beam Theory for Composite and Sandwich Beams , 2009 .

[21]  M. Gherlone On the Use of Zigzag Functions in Equivalent Single Layer Theories for Laminated Composite and Sandwich Beams: A Comparative Study and Some Observations on External Weak Layers , 2013 .

[22]  E. Carrera On the use of the Murakami's zig-zag function in the modeling of layered plates and shells , 2004 .

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

[24]  R. P. Shimpi,et al.  A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates , 2002 .

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

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