REFINED HIGHER ORDER FINITE ELEMENT MODELS FOR THERMAL BUCKLING OF LAMINATED COMPOSITE AND SANDWICH PLATES

Two refined higher order theories, one that neglects and the other that takes into account the effect of transverse normal deformation, are used to develop two discrete finite element models for the thermal buckling analysis of composite laminates and sandwiches. The two models, one with nine degrees of freedom per node and the other with eleven degrees of freedom, are based on a nine-node Lagrangian isoparametric element. The geometric stiffness matrices are developed by taking into consideration the effects of the higher order terms on the initial in-plane and transverse shear stresses. The accuracy of the present formulations is first evaluated by analyzing sample problems for which analytical three-dimensional solutions exist in the literature. Numerical results are presented for the first time for sandwich plates, demonstrating the importance and accuracy of the higher order theory in comparison to first-order theory. Some new results are also given for sandwich plates with angle-ply composite face sheets, showing the effects of various boundary conditions and of variations in geometric and lamina tion parameters on critical temperature.     

THERMOELASTIC ANALYSTS OF LAMINATED PLATES. 2: ANTISYMMETRIC CROSS-PLY AND ANGLE-PLY LAMINATES

Thermal deformations and stress resultants in rectangular, antisymmetric cross-ply and angle-ply laminates are investigated. Exact solutions are obtained for the response of simply supported plates to general three-dimensional temperature variations. To illustrate the thermoelastic behavior, deflections are computed for fiber-reinforced laminates undergoing constant and linearly varying temperature fields. Thermal membrane-bending coupling is found to be significant when the total number of layers is small, but it rapidly becomes unimportant as the number of layers within a plate of a given thickness increases.     

THERMAL BUCKLING AND POSTBUCKLING OF SYMMETRICALLY LAMINATED COMPOSITE PLATES

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Ray-leigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a ( ±45/0/90) _s and a ( ± 45/0₂ ) _s, under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axes not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports defied more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.     

THERMAL BENDING ANALYSIS OF COMPOSITE LAMINATED CYLINDRICAL SHELLS USING A REFINED FIRST-ORDER THEORY

The problem of deducing two-dimensional theory from three-dimensional theory for a thermoelastic isotropic body is investigated. Based on thermoelasticity theory, the refined plate theory is derived by using Biot's solution of thermoelasticity and Lur'e method without ad hoc assumptions. For the homogeneous boundary conditions, the exact equations and solutions are derived and the equations can be decomposed into four governing differential equations: the biharmonic equation, the shear equation, the transcendental equation and the temperature equation. Moreover, the approximate equations and solutions for the plate under anti-symmetrical transverse loadings and temperature distribution are derived directly from the refined plate theory. By omitting coupling effect and higher-order terms, the refined plate theory can be degenerated into other well-known elastic and thermoelastic theoretical models.     

THERMAL STRESSES IN LAMINATED BEAMS

This paper considers laminated beams consisting of layers of different materials fastened together by thin adhesives. The stresses that result from subjecting the beam to temperature stimuli are calculated. The problem is treated by two-dimensional elasticity theory in conjunction with the variational theorem of complementary energy. A pair of governing differential equations is developed, and boundary conditions concerning stress-free surfaces and ends of the beam are satisfied. The calculation of the distributions of interlaminar normal and shear stresses shows that high stress intensity occurs in the end zones of the beam. Thus, the satisfaction of end conditions is of prime importance in the analysis of laminated structural elements. Delamination failure-when it occurs - will probably start at the ends of the beam, This agrees with observed failures of laminated structural elements subjected to stress-free end conditions.     

INELASTIC THERMAL BUCKLING OF METAL MATRIX LAMINATED PLATES

A method is proposed for determining the critical temperature changes that cause inelastic thermal bifurcation buckling of metal matrix composite plates. The inelastic behavior of the metallic matrix is described by an elastic-viscoplastic temperature-dependent constitutive law; the fibers are allowed to be either elastic or elastic-viscoplastic material. The approach is based on the applied thermal load and the history-dependent instantaneous effective thermomechanical properties of metal matrix composites, which are established by a micromechanical analysis. The method is illustrated by the prediction of the inelastic thermal buckling of SiC/Ti metal matrix angle-ply laminated plates by employing the classical and first-order shear deformable laminated plate theories.     

BUCKLING OF PLATES DUE TO SELF-EQUILIBRATED THERMAL STRESSES

Thermal buckling of load-free supported plates is considered. Especially the influence of the distribution of the applied temperature field on buckling modes and proper values is investigated, ft turns out that fields of temperature‐shock type are most critical and lead to the lowest proper values of buckling.     

THERMAL TEMPERING SIMULATION OF GLASS PLATES: INNER AND EDGE RESIDUAL STRESSES

Narayanaswamy's model is used to describe the thermomechanical behavior of glass. It includes both stress relaxation (to take into account the viscous aspect of glass) and structural relaxation (to take into account the structure state of glass). The necessary thermal and mechanical characteristics are given for the float soda-lime silicate glass.

The thermal tempering of thin glass plates is simulated. Transient and residual stresses are given for the inner part of the plate. Computational results are compared with experimental results of previous works. This comparison validates Naranaswamy's model associated with material characteristics given previously.

The edge effect (variation of stresses close to the edges) is described for thin plates. The thermal tempering of thick plates is simulated, and computational results are validated with optical measurements and a fractographic analysis.     

STUDY ON LOCAL DELAMINATED THERMAL BUCKLING OF COMPOSITE LAMINATED PLATES

Based on the Whitcomb delaminated buckling model, a Rayleigh-Ritz analysis is presented to study the local thermal buckling problem of elliptical, rectangular, triangular, and lemniscate delaminations in a symmetric composite laminated plate. The critical temperatures of the laminated plate with various shaped local delaminations and different stacking patterns are obtained by utilizing the energy principle. The geometrical axis of various shapes of local delamination is arbitrary. The stacking sequence of base laminated plates is symmetric, but the stacking sequence of the sublayer is asymmetric. Finally, our experimental study on the mechanism of delaminated buckling failure in a laminated plate with a single elliptical and rectangular delamination near the surface of the laminated plate under thermal load was accomplished. Analytical predictions for the critical temperature yielding the local delamination buckling are shown to correlate well with experimental results for a number of different delamination shapes.     

MIXED VARIATIONAL FORMULA FOR THE THERMAL BENDING OF LAMINATED PLATES

A mixed variational formula based upon Hamilton's principle is obtained including the thermomechanical action of composite structures. Based on this formula, a linear thermomechanical composite plate model is presented. The model accounts for a Mindlin-type assumption on displacements and stresses in consistence with general surface conditions. So the rationale for the shear correction factor is obviated. Governing equations of orthotropic composite plates subjected to thermal and mechanical loading are derived. A wide variety of results are presented. The validity of the model is demonstrated by comparison with solutions available in the literature. The present results are in good agreement with the results of others.     

TRANSIENT VARIATIONS OF THERMAL STRESSES AND THE RESULTING RESIDUAL STRESSES WITHIN A THIN PLATE DURING WELDING PROCESSES

Variations of thermal and residual stresses are investigated inside a thin mild steel plate during welding processes. The temperature distribution is determined analytically using Green's functions. Transient thermal stresses developed within the plate are computed numerically. The resulting residual stresses, which remain after cooling of the plate, are found based on a method presented originally by Tall (L. Tall, Welding Journal, vol. 43, pp. 10–23, 1964). It is found that welding speed and heat source intensity are the main factors that affect the residual stress formation in the plate.     

BEHAVIOR OF THERMAL STRESSES IN A RAPIDLY HEATED THIN PLATE

Using the hyperbolic heat conduction model, thermal stresses generated within a rapidly heated thin metal plate are investigated numerically. The effects of different parameters such as the form, duration, amplitude, and penetration depth of the heating source on the temperature, thermal moment, deflection, and thermal stresses are studied. It is found that under ultra-fast heating of very thin plates, the hyperbolic heat conduction model must be adopted to model the thermal behavior.     

THERMAL STRESSES IN A RAPIDLY HEATED PLATE USING THE PARABOLIC TWO-STEP HEAT CONDUCTION EQUATION

This work studies the thermal stresses generated within a rapidly heated thin metal plate when a parabolic two-step heat conduction equation is used. The effect of different design parameters on the thermal and stress behavior of the plate is investigated.     

FLEXURAL CHARACTERISTICS AND LAYUP OPTIMIZATION OF LAMINATED COMPOSITE PLATES UNDER HYGROTHERMAL CONDITIONS USING LAMINATION PARAMETERS

The flexural characteristics and layup optimization of laminated composite plates are examined in environmental conditions of temperature and moisture. The deflection of laminated composite plates is analyzed in the design space of 12 lamination parameters. The layup optimization for minimizing the deflection of laminated composite plates is carried out using all 12 lamination parameters as design variables. Mathematical programming methods are used for optimization. In hygrothermal conditions, the maximum deflection of laminated composite plates with in-plane hygrothermal stresses can be reduced by optimized nonsymmetric laminate configurations.     

DEFORMATION CONTROL OF LAMINATED COMPOSITE PLATES CONTAINING PIEZOELECTRIC LAYERS UNDER THERMAL LOADING

A composite plate containing piezoceramics on both the upper and bottom surfaces is considered. Based on the piezoelectricity with consideration for the coupling between the strain field and the electric field, a finite element formulation is developed. An eight-node three-dimensional brick element is used, and three-dimensional incompatible modes are introduced to take into account the bending behavior of the structure. The response of the structure and the sensor electrical outputs subjected to thermal loading as well as the required voltage that should be applied to reduce the deflection resulting from thermal loading are analyzed. In addition, this study also analyzes the effect of coupling between the strain field and the electrical field. It shows that the coupling effect may not be negligible; the larger the piezoelectric constant, or the thinner the main structure, the larger the coupling effect will be.     

THERMAL STRESSES IN AN INFINITE PLATE WITH TWO ROWS OF HOLES

Abstract

A theoretical method is presented for a two-dimensional, steady thermoelastic problem of perforated plates with two rows of holes. The analysis is developed by the complex variable approach. The numerical results for stress concentration factors are given in the form of curves for a wide range of diameter/pitch. The extension of the present method to holes of arbitrary shape, number, and array is quite straightforward.     

THERMALLY INDUCED VIBRATION OF CROSS-PLY LAMINATED SHALLOW ARCHES

The dynamic response of simply supported cross-ply laminated shallow arches exposed to rapid heating is examined. The classical laminated arch theory, involving two coupled partial differential equations, is used. The equations of motion are converted into a linear system of ordinary differential equations using state variables. A closed-form solution for the induced flexural vibrations is obtained. As a demonstrative example, histories of deflection of graphite-reinforced aluminum arches are presented.     

THERMOELASTIC VIBRATIONS OF A LAMINATED RECTANGULAR PLATE SUBJECTED TO A THERMAL SHOCK

In this work the response of a rectangular, simply supported, symmetrically laminated, cross-ply composite plate subjected to a thermal shock is developed. The analysis includes the interaction between the strain and temperature fields and investigates the effect of accounting for the orthotropic material properties in the governing elastic and thermal equations. The resulting solution for the vibration of the plate is compared to a previous analysis of a homogeneous, isotropic, rectangular plate. Comparison indicates that while the solutions have similar forms, there are two key quantitative differences between them.     

THERMAL STRESSES IN A NONHOMOGENEOUS THICK PLATE UNDER STEADY DISTRIBUTION OF TEMPERATURE

This paper is concerned with a method for calculating the thermal-stress distribution in a nonhomogeneous medium whose shear modulus and coefficient of thermal expansion are assumed to be functions of z. The solution of the problem is determined by using displacement functions. A solution is then derived for the thermal-stress distribution in a nonhomogeneous, thick elastic plate under steady distribution of the surface temperature. Numerical results are presented.