Temperature Profile Influence on Layered Plates Response Considering Classical and Advanced Theories

A study on the influence of the through-the-thickness temperature profile T(z) on the thermomechanical response of multilayered anisotropic thick and thin plates has been conducted. The heat conduction problem is solved, and the temperature variation T c (z) is then calculated. The governing thermomechanical equations of multilayered plates are written considering a large variety of classical and advanced or zigzag theories into account. The principle of virtual displacement and the Reissner mixed variational theorem are employed. Linear, up to fourth-order expansions in z are retained for the assumed transverse stress and displacement fields. As a result, more than 20 plate theories are compared. The numerical investigation is restricted to orthotropic layered plates with harmonic in-plane distribution of both thermal loadings and unknown variables. Four sample plate problems are treated that are related to plates made of isotropic and/or orthotropic layers that are loaded by different top-bottom plate surface temperature conditions. Comparison is made to results related to a linear profile T a (z), which is usually assumed in open literature. The following is concluded: Thick plates could exhibit a layerwise form temperature profile T c (z). T a (z) case is approached for thin plate geometries. The use of linear temperature profile leads to large errors in tracing the response of thick plate geometries. The accuracy of plate theories is affected to great extent by the form of temperature variation T(z). Refinements of classical plate theories can be meaningless unless the calculated T c (z) is introduced. The layerwise form of T c (z) would require layerwise assumptions for stresses and/or displacements. Plate theories that neglect transverse normal strains lead to very inaccurate results in both thick and thin plates analysis. At least a parabolic expansion for transverse displacement is required to capture transverse normal thermal strains that vary linearly along the plate thickness.

[1]  E. Reissner.  On a certain mixed variational theorem and a proposed application , 1984 .

[2]  M. N. Bapu Rao.  Three dimensional analysis of thermally loaded thick plates , 1979 .

[3]  H. Murakami,et al.  Assessment of plate theories for treating the thermomechanical response of layered plates , 1993 .

[4]  Santosh Kapuria,et al.  An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading , 2003 .

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

[6]  Xu Zhou,et al.  Dynamic Responses of Smart Composites Using a Coupled Thermo-Piezoelectric -Mechanical Model , 2000 .

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

[8]  Ahmed K. Noor,et al.  Computational Models for High-Temperature Multilayered Composite Plates and Shells , 1992 .

[9]  John Argyris,et al.  Recent Advances in Computational Thermostructural Analysis of Composite Plates and Shells With Strong Nonlinearities , 1997 .

[10]  T. K. Varadan,et al.  THERMOELASTIC SOLUTIONS FOR ORTHOTROPIC AND ANISOTROPIC COMPOSITE LAMINATES , 1996 .

[11]  T. R. Tauchert,et al.  Thermally Induced Flexure, Buckling, and Vibration of Plates , 1991 .

[12]  Erasmo Carrera,et al.  AN ASSESSMENT OF MIXED AND CLASSICAL THEORIES FOR THE THERMAL STRESS ANALYSIS OF ORTHOTROPIC MULTILAYERED PLATES , 2000 .

[13]  Gyula Greschik,et al.  Sensitivity Study of Precision Pressurized Membrane Reflector Deformations , 2001 .

[14]  E. Reissner.  On a mixed variational theorem and on shear deformable plate theory , 1986 .

[15]  Xu Zhou,et al.  A higher order temperature theory for coupled thermo-piezoelectric-mechanical modeling of smart composites , 2000 .

[16]  Erasmo Carrera,et al.  Single- vs Multilayer Plate Modelings on the Basis of Reissner's Mixed Theorem , 2000 .

[17]  T. K. Varadan,et al.  A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates , 1999 .

[18]  E. Carrera.  Layer-Wise Mixed Models for Accurate Vibrations Analysis of Multilayered Plates , 1998 .

[19]  Thermal stress analysis of laminate using higher-order theory in each layer , 1989 .

[20]  E. Carrera.  A study of transverse normal stress effect on vibration of multilayered plates and shells , 1999 .

[21]  K. M. Rao,et al.  Three dimensional exact solution of thermal stresses in rectangular composite laminate , 1994 .

[22]  Erasmo Carrera,et al.  Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis , 1998 .

[23]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .