A GENERAL NON-LINEAR THIRD-ORDER THEORY OF PLATES WITH MODERATE THICKNESS

A review of all third-order, two-dimensional technical theories of plates is presented and their equivalence is established. All third-order theories published during the last two decades are shown to be based on the same displacement field, contrary to the claims by many authors. Consequently, all variationally derived plate theories are a special case of the third-order plate theory published by the author in 1984. A consistent-strain, third-order, displacement field is proposed herein and associated, variationally consistent, theory is developed.

[1]  A. Bhimaraddi.  Static and transient response of rectangular plates , 1987 .

[2]  H. Hencky,et al.  Über die Berücksichtigung der Schubverzerrung in ebenen Platten , 1947 .

[3]  Liviu Librescu,et al.  Analytical solution of a refined shear deformation theory for rectangular composite plates , 1987 .

[4]  J. N. Reddy,et al.  On the forced motions of antisymmetric cross-ply laminated plates , 1989 .

[5]  A. V. Krishna Murty,et al.  Flexure of composite plates , 1987 .

[6]  J. N. Reddy,et al.  Energy and variational methods in applied mechanics , 1984 .

[7]  A. B. Basset.  On the Extension and Flexure of Cylindrical and Spherical Thin Elastic Shells , 1889 .

[8]  F. B. Hildebrand,et al.  Notes on the foundations of the theory of small displacements of orthotropic shells , 1949 .

[9]  J. N. Reddy,et al.  A Small Strain and Moderate Rotation Theory of Elastic Anisotropic Plates , 1987 .

[10]  J. N. Reddy,et al.  EFFECTS OF SHEAR DEFORMATION AND ANISOTROPY ON THE THERMAL BENDING OF LAYERED COMPOSITE PLATES , 1980 .

[11]  L. K. Stevens,et al.  A Higher Order Theory for Free Vibration of Orthotropic, Homogeneous, and Laminated Rectangular Plates , 1984 .

[12]  J. N. Reddy,et al.  On the Generalization of Displacement-Based Laminate Theories , 1989 .

[13]  G. Kirchhoff,et al.  Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. , 1850 .

[14]  N. Huffington.  RESPONSE OF ELASTIC COLUMNS TO AXIAL PULSE LOADING , 1963 .

[15]  S. T. Chow,et al.  Buckling of Shear-Deformable Plates , 1987 .

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

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

[18]  M. Poisson.  Mémoire sur l'équilibre et le mouvement des corps élastiques , 1828 .

[19]  A. V. Krishna Murty.  Higher order theory for vibrations of thick plates , 1977 .

[20]  J. Reddy,et al.  Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory , 1985 .

[21]  J. N. Reddy,et al.  A refined nonlinear theory of plates with transverse shear deformation , 1984 .

[22]  J. Reddy,et al.  Lévy Type Solutions for Symmetrically Laminated Rectangular Plates Using First-Order Shear Deformation Theory , 1987 .

[23]  E. Reissner.  ON THE THEORY OF BENDING OF ELASTIC PLATES , 1944 .

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

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

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