Large displacement analysis of sandwich plates and shells with symmetric/asymmetric lamination

Novel zigzag function for sandwich plates/shells with symmetric/asymmetric section.New through-thickness distribution of transverse shear strains for sandwich section.Co-rotational approach for large displacement small strain nonlinear analysis.Proposed 2D 'shell' coordinate system for effective treatment of zigzag parameters.Examples highlight benefits of new model for symmetric/asymmetric sandwich shells. This paper proposes a kinematic model for sandwich plates and shells, utilising a novel zigzag function that is effective for symmetric and asymmetric cross-sections, and employing a piecewise through-thickness distribution of the transverse shear strain. The proposed model is extended to large displacement analysis using a co-rotational framework, where a 2D local shell system is proposed for the direct coupling of additional zigzag parameters. A 9-noded co-rotational shell element is developed based on the proposed approach, which utilises the MITC method for overcoming locking effects. Several linear/nonlinear analysis examples of sandwich structures demonstrate the effectiveness of the proposed approach.

[1]  Tarun Kant,et al.  Higher-order shear deformable theories for flexure of sandwich plates—Finite element evaluations , 1988 .

[2]  Hamdan N. Al-Ghamedy,et al.  Finite element formulation of a third order laminated finite rotation shell element , 2002 .

[3]  Bassam A. Izzuddin,et al.  An enhanced co‐rotational approach for large displacement analysis of plates , 2005 .

[4]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[5]  Abdul Hamid Sheikh,et al.  An improved C0 FE model for the analysis of laminated sandwich plate with soft core , 2012 .

[6]  Hung Nguyen-Xuan,et al.  Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory , 2013 .

[7]  Erasmo Carrera,et al.  Multilayered shell finite element with interlaminar continuous shear stresses : a refinement of the Reissner-Mindlin formulation , 2000 .

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

[9]  António J.M. Ferreira,et al.  Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter , 2008 .

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

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

[12]  C. Smith.  Large deflections of circular sandwich plates. , 1968 .

[13]  Luciano Demasi,et al.  2D, Quasi 3D and 3D Exact Solutions for Bending of Thick and Thin Sandwich Plates , 2008 .

[14]  Erasmo Carrera,et al.  An assessment of Mixed and Classical Theories on Global and Local Response of Multilayered, Orthotropic Plates , 2000 .

[15]  M. L. Bucalém,et al.  Higher‐order MITC general shell elements , 1993 .

[16]  Phill-Seung Lee,et al.  The quadratic MITC plate and MITC shell elements in plate bending , 2010, Adv. Eng. Softw..

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

[18]  Salim Belouettar,et al.  Review and assessment of various theories for modeling sandwich composites , 2008 .

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

[20]  L. Vu-Quoc,et al.  A 9-node co-rotational quadrilateral shell element , 2008 .

[21]  E. Carrera,et al.  An evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells , 1997 .

[22]  M. A. Crisfield,et al.  A unified co-rotational framework for solids, shells and beams , 1996 .

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

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

[25]  Klaus-Jürgen Bathe,et al.  3D-shell elements for structures in large strains , 2013 .

[26]  E. Carrera.  A refined multilayered finite-element model applied to linear and non-linear analysis of sandwich plates , 1998 .

[27]  E. Carrera.  Developments, ideas, and evaluations based upon Reissner’s Mixed Variational Theorem in the modeling of multilayered plates and shells , 2001 .

[28]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[29]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[30]  Phill-Seung Lee,et al.  Towards improving the MITC9 shell element , 2003 .

[31]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[32]  B. Izzuddin,et al.  Nonlinear dynamic analysis of framed structures , 1990 .

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

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

[35]  J. N. Reddy,et al.  On refined computational models of composite laminates , 1989 .

[36]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[37]  E. Carrera,et al.  An investigation of non-linear dynamics of multilayered plates accounting for C0z requirements , 1998 .

[38]  E. Carrera.  Theories and Finite Elements for Multilayered Plates and Shells:A Unified compact formulation with numerical assessment and benchmarking , 2003 .

[39]  E. Carrera.  An Improved Reissner-Mindlin-Type Model for the Electromechanical Analysis of Multilayered Plates Including Piezo-Layers , 1997 .

[40]  K. Wisniewski,et al.  Two improvements in formulation of nine‐node element MITC9 , 2013 .

[41]  Egor P. Popov,et al.  Nonlinear Finite Element Analysis of Sandwich Shells of Revolution , 1972 .

[42]  K. Bathe.  Finite Element Procedures , 1995 .

[43]  B. Izzuddin,et al.  Bisector and zero‐macrospin co‐rotational systems for shell elements , 2016 .

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