Accurate transverse stress evaluation in composite/sandwich thick laminates using a C0 HSDT and a novel post-processing technique

Abstract An efficient method for accurate evaluation of through-the-thickness distribution of transverse stresses in thick composite and sandwich laminates, using a displacement-based C 0 higher-order shear deformation theory (HSDT), is presented. The technique involves a least square of error (LSE) method applied to the 3D equilibrium equations at the post-processing phase, after a primary finite element analysis is performed using the HSDT. This is distinctly different from the conventional method of integrating the 3D equilibrium equations, for transverse stress recovery in composite laminates during post-processing. Competence of the technique is demonstrated in the numerical examples through comparison with results from first-order shear deformation theory (FSDT), another HSDT and those from analytical and 3D elasticity solutions available in literature.

[1]  Satya N. Atluri,et al.  Postbuckling analysis of stiffened laminated composite panels, using a higher-order shear deformation theory , 1992 .

[2]  Marco Di Sciuva,et al.  A refined transverse shear deformation theory for multilayered anisotropic plates. , 1984 .

[3]  E. Reissner,et al.  Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates , 1961 .

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

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

[6]  R. B. Nelson,et al.  A Refined Theory for Laminated Orthotropic Plates , 1974 .

[7]  M. Levinson,et al.  An accurate, simple theory of the statics and dynamics of elastic plates , 1980 .

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

[9]  Dahsin Liu,et al.  An Overall View of Laminate Theories Based on Displacement Hypothesis , 1996 .

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

[11]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

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

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

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

[15]  C. Sun,et al.  A higher order theory for extensional motion of laminated composites , 1973 .

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

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

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

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

[20]  J. N. Reddy,et al.  A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates , 1992 .

[21]  Charles W. Bert,et al.  A critical evaluation of new plate theories applied to laminated composites , 1984 .

[22]  J. N. Reddy,et al.  A review of refined theories of laminated composite plates , 1990 .

[23]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[24]  Tarun Kant,et al.  A Simple Finite Element Formulation of a Higher-order Theory for Unsymmetrically Laminated Composite Plates , 1988 .

[25]  R. Christensen,et al.  A HIGH-ORDER THEORY OF PLATE DEFORMATION, PART 1: HOMOGENEOUS PLATES , 1977 .

[26]  Erasmo Carrera,et al.  A unified formulation to assess theories of multilayered plates for various bending problems , 2005 .

[27]  A. Sheikh,et al.  A FINITE ELEMENT FORMULATION FOR THE ANALYSIS OF LAMINATED COMPOSITE SHELLS , 2004 .

[28]  P. M. Naghdi,et al.  ON THE THEORY OF THIN ELASTIC SHELLS , 1957 .

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