Vibration of laminated composites and sandwich shells based on higher order zigzag theory

Free vibration response of laminated composite and sandwich shell is studied by using an efficient 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders’ approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at the interfaces in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C0 finite element formulation has been done efficiently to overcome the problem of C1 continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells, etc., besides normal curvature shells like cylindrical, and spherical shells. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.

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

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

[3]  Bhanu Singh,et al.  Vibration of Sandwich Plates with Random Material Properties using Improved Higher-Order Zig-Zag Theory , 2010 .

[4]  A. Leissa,et al.  Vibration of shells , 1973 .

[5]  K. Liew,et al.  A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory , 1995 .

[6]  R. B. Corr,et al.  A simultaneous iteration algorithm for symmetric eigenvalue problems , 1976 .

[7]  M. S. Qatu.  Review of shallow shell vibration research , 1992 .

[8]  Jianqiao Ye,et al.  Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up , 1994 .

[9]  Rakesh Kumar Khare,et al.  Higher-order Closed-form Solutions for Thick Laminated Sandwich Shells , 2005 .

[10]  K. Liew,et al.  Vibration of Thick Doubly-Curved Stress Free Shallow Shells of Curvilinear Planform , 1997 .

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

[12]  Holm Altenbach,et al.  Theories for laminated and sandwich plates , 1998 .

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

[14]  A. Noor,et al.  Assessment of computational models for sandwich panels and shells , 1995 .

[15]  K. M. Liew,et al.  A higher order theory for vibration of shear deformable cylindrical shallow shells , 1995 .

[16]  Liviu Librescu,et al.  Recent developments in the modeling and behavior of advanced sandwich constructions: a survey , 2000 .

[17]  Chuanzeng Zhang,et al.  A meshfree model without shear-locking for free vibration analysis of first-order shear deformable plates , 2011 .

[18]  K. M. Liew,et al.  Research developments in analyses of plates and shells , 1993 .

[19]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[20]  A. E. H. Love,et al.  The Small Free Vibrations and Deformation of a Thin Elastic Shell , 1887 .

[21]  J. N. Bandyopadhyay,et al.  Static and Free Vibration Analyses of Laminated Shells using a Higher-order Theory , 2008 .

[22]  N. Ganesan,et al.  Analysis of active damping in composite laminate cylindrical shells of revolution with skewed PVDF sensors/actuators , 2000 .

[23]  K. M. Liew,et al.  A pb-2 Ritz Formulation for Flexural Vibration of Shallow Cylindrical Shells of Rectangular Planform , 1994 .

[24]  Dimitris A. Saravanos,et al.  Coupled mechanics and finite element for non‐linear laminated piezoelectric shallow shells undergoing large displacements and rotations , 2006 .

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

[26]  Ahmed K. Noor,et al.  Computational Models for Sandwich Panels and Shells , 1996 .

[27]  R. A. S. Moreira,et al.  A generalized layerwise finite element for multi-layer damping treatments , 2006 .

[28]  Wang An.  Vibration and transverse stresses of laminated cylindrical shells , 2000 .

[29]  K. M. Liew,et al.  Three-dimensional vibration analysis of spherical shell panels subjected to different boundary conditions , 2002 .

[30]  B. P. Patel,et al.  Dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells using higher-order theory , 2002 .

[31]  Yavuz Başar,et al.  Free-vibration analysis of thin/thick laminated structures by layer-wise shell models , 2000 .

[32]  K. M. Liew,et al.  Vibration of Shallow Shells: A Review With Bibliography , 1997 .

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

[34]  K. M. Liew,et al.  A Higher-Order Theory for Vibration of Doubly Curved Shallow Shells , 1996 .

[35]  Mark A. Bradford,et al.  Vibration analysis of simply supported plates of general shape with internal point and line supports using the Galerkin method , 2000 .

[36]  K. M. Liew,et al.  Vibratory Behavior of Doubly Curved Shallow Shells of Curvilinear Planform , 1995 .

[37]  M. S. Qatu.  LITERATURE REVIEW analysis of the shock and vibration literature: Review of Shallow Shell Vibration Research , 1992 .