A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core

Abstract A new finite element (FE) model has been developed based on higher order zigzag theory (HOZT) for the static analysis of laminated sandwich beam with soft core. In this theory, the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to vary quadratically within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. A C 0 quadratic beam finite element is implemented to model the HOZT for the present analysis. Numerical examples covering different features of laminated composite and sandwich beams are presented to illustrate the accuracy of the present model. Many new results are also presented which should be useful for future research.

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

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

[3]  Ronald C. Averill,et al.  An improved theory and finite-element model for laminated composite and sandwich beams using first-order zig-zag sublaminate approximations , 1997 .

[4]  Ugo Icardi,et al.  A three-dimensional zig-zag theory for analysis of thick laminated beams , 2001 .

[5]  Dahsin Liu,et al.  An interlaminar stress continuity theory for laminated composite analysis , 1992 .

[6]  R. P. Shimpi,et al.  A new layerwise trigonometric shear deformation theory for two-layered cross-ply beams , 2001 .

[7]  Masoud Tahani,et al.  Analysis of laminated composite beams using layerwise displacement theories , 2007 .

[8]  Dahsin Liu,et al.  An Interlaminar Shear Stress Continuity Theory for Both Thin and Thick Composite Laminates , 1992 .

[9]  C. T. Sun,et al.  A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates , 1987 .

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

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

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

[13]  Bhanu Singh,et al.  An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core , 2008 .

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

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

[16]  E. Carrera.  C0 REISSNER–MINDLIN MULTILAYERED PLATE ELEMENTS INCLUDING ZIG-ZAG AND INTERLAMINAR STRESS CONTINUITY , 1996 .

[17]  Yeoshua Frostig.  Classical and high-order computational models in the analysis of modern sandwich panels , 2003 .

[18]  K. H. Lee,et al.  An improved zig-zag model for the bending of laminated composite shells , 1990 .

[19]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[20]  M Discuiva.  AN IMPROVED SHEAR DEFORMATION THEORY FOR MODERATELY THICK MULTILAYERED ANISOTROPIC SHELLS AND PLATES , 1987 .

[21]  D. Roy Mahapatra,et al.  Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities , 2002 .

[22]  Ronald C. Averill,et al.  First-order zig-zag sublaminate plate theory and finite element model for laminated composite and sandwich panels , 2000 .

[23]  Rakesh K. Kapania,et al.  A shear-deformable beam element for the analysis of laminated composites , 2007 .

[24]  Abdul Hamid Sheikh,et al.  A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates , 2003 .

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

[26]  Y. M. Desai,et al.  Hybrid-interface finite element for laminated composite and sandwich beams , 2007 .

[27]  Venkat Aitharaju.  C0 Zigzag Kinematic Displacement Models for the Analysis of Laminated Composites , 1999 .

[28]  Ronald C. Averill,et al.  Development of simple, robust finite elements based on refined theories for thick laminated beams , 1996 .

[29]  P. Subramanian,et al.  Dynamic analysis of laminated composite beams using higher order theories and finite elements , 2006 .

[30]  Hiroyuki Matsunaga,et al.  Interlaminar stress analysis of laminated composite beams according to global higher-order deformation theories , 2002 .

[31]  R. C. Averill,et al.  Thick beam theory and finite element model with zig-zag sublaminate approximations , 1996 .

[32]  J. Reddy,et al.  THEORIES AND COMPUTATIONAL MODELS FOR COMPOSITE LAMINATES , 1994 .

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

[34]  J. N. Reddy,et al.  An exact solution for the bending of thin and thick cross-ply laminated beams , 1997 .

[35]  Ugo Icardi,et al.  Applications of Zig-Zag Theories to Sandwich Beams , 2003 .

[36]  Srinivasan Gopalakrishnan,et al.  A refined higher order finite element for asymmetric composite beams , 2005 .

[37]  R. P. Shimpi,et al.  A beam finite element based on layerwise trigonometric shear deformation theory , 2001 .