Assessment of computational models for multilayered anisotropic plates

A study is made of the effects of variation in the lamination and geometric parameters of multilayered anisotropic (nonorthotropic) plates on the accuracy of the static and vibrational responses predicted by eight modeling approaches, based on two-dimensional shear-deformation theories. Two key elements distinguish the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the exact three-dimensional elasticity solutions, and (2) quantities compared are not limited to gross response characteristics (e.g. vibration frequencies, strain energy components, average through-the-thickness displacements and rotations), but include detailed through-the-thickness distributions of displacements, stresses and strain energy densities. The modeling approaches considered include first-order shear-deformation theory (with five displacement parameters to characterize the deformation in the thickness direction); first-order theory with the transverse normal stresses and strains included (six displacement parameters); two higher-order theories (with 11 and 18 displacement parameters); a simplified higher-order theory (with five displacement parameters); discrete-layer theory (with piecewise linear variation of the in-plane displacements in the thickness direction); simplified discrete-layer theory with the continuity of transverse stresses imposed at layer interfaces to reduce the number of displacement parameters to five; and a predictor-corrector approach, used in conjunction with the first-order shear-deformation theory (with five displacement parameters in the predictor phase). Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective among the eight modeling approaches considered. For antisymmetrically laminated rectangular plates the response quantities obtained by the predictor-corrector approach are shown to be in close agreement with exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. The potential of this approach for predicting the response of multilayered anisotropic plates with complicated geometry is also discussed.

[1]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[2]  Ahmed K. Noor,et al.  Stress and free vibration analyses of multilayered composite plates , 1989 .

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

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

[5]  J. N. Reddy,et al.  Dynamic response of antisymmetric angle-ply laminated plates subjected to arbitrary loading , 1988 .

[6]  N. J. Pagano,et al.  Dynamic characteristics of composite laminates , 1972 .

[7]  J. Whitney,et al.  Shear Correction Factors for Orthotropic Laminates Under Static Load , 1973 .

[8]  Stanley B. Dong,et al.  On the Theory of Laminated Anisotropic Shells and Plates , 1962 .

[9]  A. W. Leissa,et al.  Analysis of Heterogeneous Anisotropic Plates , 1969 .

[10]  C. Sun,et al.  Theories for the Dynamic Response of Laminated Plates , 1973 .

[11]  D. E. McFarland,et al.  Analysis of plates , 1972 .

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

[13]  Tarun Kant,et al.  A CONSISTENT REFINED THEORY FOR FLEXURE OF A SYMMETRIC LAMINATE , 1987 .

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

[15]  V. Polyakov,et al.  Shear effects during bending of oriented glass-reinforced plastics , 1965 .

[16]  S. Srinivas,et al.  An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates , 1970 .

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

[18]  T. J. Kozik,et al.  Transverse shear and normal stresses in laminated plates , 1984 .

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

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

[21]  T. Chow,et al.  On the Propagation of Flexural Waves in an Orthotropic Laminated Plate and Its Response to an Impulsive Load , 1971 .

[22]  Charles W. Bert,et al.  Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates , 1978 .

[23]  J. Whitney.  Structural Analysis of Laminated Anisotropic Plates , 1987 .

[24]  Victor Birman,et al.  Dynamic Instability of Shear Deformable Antisymmetric Angle-Ply Plates , 1987 .

[25]  J. Bleustein.  A note on the boundary conditions of toupin's strain-gradient theory , 1967 .

[26]  J. Whitney,et al.  Stress Analysis of Thick Laminated Composite and Sandwich Plates , 1972 .

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

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

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

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

[31]  J. N. Reddy,et al.  Survey of Recent Research in the Analysis of Composite Plates , 1982 .