Uniform Thermal Loading Research Articles

A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading

Due to the variation in material properties through the thickness, bifurcation buckling cannot generally occur for plates or beams made of functionally graded materials (FGM) with simply supported edges. Further investigation in this paper indicates that FGM beams subjected to an in-plane thermal loading do exhibit some unique and interesting characteristics in both static and dynamic behaviors, particularly when effects of transverse shear deformation and the temperature-dependent material properties are simultaneously taken into account. In the analysis, based on the nonlinear first-order shear deformation beam theory (FBT) and the physical neutral surface concept, governing equations for both the static behavior and the dynamic response of FGM beams subjected to uniform in-plane thermal loading are derived. Then, a shooting method is employed to numerically solve the resulting equations. The material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The effects of material constants, transverse shear deformation, temperature-dependent material properties, in-plane loading and boundary conditions on the nonlinear behavior of FGM beams are discussed in detail.

Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading

In this paper, the effect of sensitivity of randomness in system parameters on the nonlinear transverse central deflection response of laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modelled as basic random variables. A higher order shear deformation theory in the von-Karman sense is used to model the system behavior of the laminated plate. A direct iterative-based C0 nonlinear finite element method in conjunction with the first-order perturbation technique developed by the authors is extended for thermal problem to obtain the second-order response statistics, i.e., mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results of composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and transverse temperature are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading

This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to establish nonlinear equilibrium equations and buckling equilibrium equations, and analytical solutions for the limit instability and bifurcation buckling loads are obtained. It is found that the temperature influences the limit instability, bifurcation buckling and postbuckling behaviour of shallow arches significantly. The limit instability and bifurcation buckling loads increase with an increase of the temperature. A maximum temperature is shown to exist for the occurrence of bifurcation buckling of shallow arches, and when the temperature is higher than this value, bifurcation buckling of an arch is not possible. An arch geometric parameter is introduced to define switches between the limit instability and bifurcation buckling modes, and between buckling and no buckling. Formulae and methods for the calculation of the limiting values of the arch geometric parameter are developed. It is also found that the limiting values of the arch geometric parameter decrease with an increase of the temperature.

Multiobjective optimization of angle-ply laminated plates for maximum buckling load

This paper deals with multiobjective optimization of symmetrically angle-ply square laminated plates subjected to biaxial compressive and uniform thermal loads. The design objective is the maximization of the buckling load for weighted sum of the biaxial compressive and thermal loads. The design variable is the fiber orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of buckling analysis of laminated plates. The modified feasible direction (MFD) method is used for optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the effect of different weighting factors, number of layers, aspect ratios, load ratios and boundary conditions on the optimal design is investigated.

On thermoelastic fields of a multi-phase inhomogeneity system with perfectly/imperfectly bonded interfaces

The stress fields of cylindrical and spherical multi-phase inhomogeneity systems with perfect or imperfect interfaces under uniform thermal and far-field mechanical loading conditions are investigated by use of the Boussinesq displacement potentials. The radius of the core inhomogeneity and the thickness of its surrounding coatings are arbitrary. The discontinuities in the tangential and normal components of the displacement at the imperfect interfaces are assumed to be proportional to the associated tractions. In this work, for the problems where the phases of the inhomogeneity system are homogeneous, the exact closed-form thermo-elastic solutions are presented. These solutions along with a systematic numerical methodology are utilized to solve various problems of physical importance, where the constituent phases of the inhomogeneity system may be made of a number of different functionally graded (FG) and homogeneous materials, and each interface may have a perfect or imperfect boundary condition, as desired. Also, the effect of the interfacial sliding and debonding on the stress field and elastic energy of an FG-coated inhomogeneity is examined.

Thermo-elastic Stress Analysis of Injection Molding Short Glass Fiber Filled Polymer Composite Disc with Holes

The aim of this study was to find out the influences of uniform thermal loads on a composite disc having many pin/bolt holes. Polymer composite disc reinforced short glass fibers were successfully produced by using injection and compression molding techniques, and microstructural observations were carried out using an electronic microscope. A thermo-elastic stress analysis was performed utilizing a finite element method (FEM). For this reason, the thermal stresses were determined by using ANSYS software package. The circular holes were created in the disc because of observing these effects on thermal stresses. The thermal loads were applied to the disc at a uniform distribution. Due to the composite disc having different thermal expansions in radial and tangential directions, thermal stresses were created in it by applied uniform thermal loads. The magnitude of the tangential stress components was higher than the radial stress components. The magnitudes and distributions of thermal stresses on the composite disc were considerably affected by increasing the uniform temperature loads and the presence of pin/bolt holes.

Thermal-stress analysis of plates with variable fiber spacing

Plane-stress problems of a square composite plate with variable fiber spacing under a uniform thermal loading are investigated. The problem with two edges perpendicular to the fiber direction of the plate, being itself constrained from normal displacement, is first solved analytically. It is then analyzed by the energy method together with the Rayleigh–Ritz approximation, and the computed results are verified by the analytical solution showing very good agreement. Another problem, with two edges parallel to the fiber direction, the plate again being constrained from normal displacement, which is more complex and cannot be solved analytically, is tackled by the afore-mentioned numerical procedure. To investigate the effect of the variation of fiber spacing on the distributions of the displacement-component fields and the equivalent stress field, two types of variation in fiber spacing are assumed in solving the second problem.

Mechanics of Track Structure with Y-Shaped Steel Sleepers in Sharp Curves

Certain analytical elastic solution for curvilinear track section under uniform thermal loading has been proposed. Track section is composed of circular arc, transition curves and straight lines. Next step is the analysis of two-dimensional model of the track structure (stress plane, without vertical direction). The rails and the sleepers are assumed as elastic bodies. The fasteners and ballast are modeled as elastic-plastic elements. Non-linear properties of these elements are determined by comparison of numerical data with experimental results. Cyclic uniform thermal field is applied as the load of the system. Pre-buckling analysis is the basic part of the considerations. Certain remarks on the track stability, based on the previous author analyses, are also presented. It is shown that track structure with Y-shaped steel sleepers gives the possibility to use of continuous welded rail (CWR) track practically in any radius of curvature.

Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for three-dimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for three-dimensional cracks contained in functionally graded materials.

Analysis of three-dimensional interface cracks using enriched finite elements

Many important interface crack problems are inherently three-dimensional in nature, e.g., debonding of laminated structures at corners and holes. In an effort to accurately analyze three-dimensional interface fracture problems, an efficient computational technique was developed that utilizes enriched crack tip elements containing the correct interface crack tip asymptotic behavior. In the enriched element formulation, the stress intensity factors K I, K II, and K III are treated as additional degrees of freedom and are obtained directly during the finite element solution phase. In this study, the results that should be of greatest interest are obtained for semi-circular surface and quarter-circular corner cracks. Solutions are generated for uniform remote tension and uniform thermal loading, over a wide range of bimaterial combinations. Of particular interest are the free surface effects, and the influence of Dundurs’ material parameters on the strain energy release rate magnitudes and corresponding phase angles.

Properties degradation induced by transverse cracks in general symmetric laminates

This paper presents the details of a methodology for predicting the thermoelastic properties degradation in general symmetric laminates with uniform ply cracks in some or all of the 90° layers. First, a stress transfer method is derived by using the concept of state space equation. The laminate can be subjected to any combination of in-plane biaxial and shear loading, and the uniform thermal loading is also taken into account. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. By this method, a laminate may be composed of an arbitrary number of monoclinic layers and each layer may have different material property and thickness. Second, the concept of the effective thermoelastic properties of a cracked laminate is introduced. Based on the numerical solutions of specially designed loading cases, the effective thermoelastic constants of a cracked laminate can be obtained. Finally, the applications of the methodology are shown by numerical examples and compared with numerical results from other models and experiment data in the literature. It is found that the theory provides good predictions of the thermoelastic properties degradation in general symmetric laminates.

THERMAL POST-BUCKLING OF SLENDER ELASTIC RODS WITH DIFFERENT BOUNDARY CONDITIONS

This paper presents mathematical formulation, critical buckling temperature and analytical and numerical solutions for the thermal post-buckling behavior of slender rods subjected to uniform thermal load. The material is assumed to be linear elastic, homogeneous and isotropic. Furthermore, large displacements are considered hence the formulation is geometrically non-linear. Three different boundary conditions are assumed: (i) double-hinged non-movable, (ii) hinged non-movable at one end, whereas at the other end longitudinal displacement is constrained by a linear spring, and (iii) double-fixed non-movable. The governing equations are derived from geometrical compatibility, equilibrium of forces and moments, constitutive equations and strain-displacement relation, yielding a set of six first-order non-linear ordinary differential equations with boundary conditions specified at both ends, which constitutes a complex boundary value problem. The buckling and post-buckling solutions are respectively accomplished assuming infinitesimal and finite rotations. The results are presented in non-dimensional graphs for a range of temperature gradients and different values of slenderness ratios, and it is shown that this parameter governs the rod post-buckling response. The influence of the boundary conditions is evaluated through graphic results for deformed configuration, maximum deflection, maximum inclination angle and maximum curvature in the rod.

Circumferentially Cracked Bimaterial Hollow Cylinder Under Mechanical and Transient Thermal Loading

The analytical solution for the problem of a circumferential inner surface crack in an elastic, infinitely long composite hollow cylinder, made of two concentric perfectly bonded transversely isotropic cylinders is considered. Uniform axial loading and thermal loading in the form of a sudden cooling on the inner boundary are considered. Out of 10 material parameters involved, two bimaterial parameters and three material parameters for each layer upon which the stress intensity factor depends under uniform loading, are identified. The problem is reduced to a singular integral equation that is solved numerically. Stress intensity factors are presented for various values of material and geometric parameters.

Frequency Tuning Characteristics of Multi-Layered Micro-Resonators Using Thermal and Piezoelectric Actuation

Frequency tuning characteristics of the multi-layered micro-resonators have been extensively investigated by using thermal and piezoelectric actuations. Based on the layerwise displacement theory and geometric nonlinear formulation, the nonlinear deformation and its attendant vibration characteristics of un-symmetrically deposited camped-camped micro-beams under piezoelectric and thermal actuations have been analyzed. The effects of the eccentric piezoelectric actuation and uniform thermal loading on the large deflection and natural modes were discussed with respect to geometric nonlinear responses and initial imperfection. Present results show that both piezoelectric and thermal actuations can effectively tune the resonant frequencies as increasing and decreasing desired values by the alternative selection of the dominance between in-plane deformation and out-of-plane deformation.

Behaviour of thick composite tubes considering of delamination

The present paper deals with plane finite element analysis of thick composite tubes. Thick composite tubes are commonly used in marine industry and in deep-water offshore applications. Two kinds of interlaminar delamination type defect in a thick walled cylinder subjected to external pressure were confronted; an annular or ring like delamination and a strip delamination. Two finite element models were developed to predict the strain energy release rate at the delamination fronts. In these models the effects of the processing history of the composite material in the form of a uniform thermal load were also included to simulate the state of the residual stress in the composite. The considered defects are studied by means of the effect of buckling, investigating the annular and the strip delamination buckling, and the subsequent loss of load carrying capacity of the delaminated region.

Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.

Nonlinear Bending Response of Functionally Graded Plates Under Thermal Loads

ABSTRACT Nonlinear bending analysis of functionally graded plates subjected to uniform pressure and thermal loads is investigated using a 3-D finite element method. Material properties are varied continuously in the thickness direction according to a simple power law distribution. A three-dimensional solid element is used for more accurate modeling of material properties and temperature field in the thickness direction. The Green–Lagrange nonlinear strain-displacement relation is used to account for large deflection due to uniform pressure and thermal loads and the incremental formulation is applied for nonlinear analysis. The thermal loads are assumed as uniform, linear and sinusoidal temperature rises across the thickness direction. In numerical studies, the nonlinear bending responses of Al2O3-Ni FGM plates due to temperature field, volume fraction distribution, and system geometric parameters are presented, in detail.

Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites

Shape memory alloy hybrid composites with adaptive-stiffening or morphing functions are simulated using finite element analysis. The composite structure is a laminated fiber-polymer composite beam with embedded SMA ribbons at various positions with respect to the neutral axis of the beam. Adaptive stiffening or morphing is activated via selective resistance heating of the SMA ribbons or uniform thermal loads on the beam. The thermomechanical behavior of these composites was simulated in ABAQUS using user-defined SMA elements. The examples demonstrate the usefulness of the methods for the design and simulation of SMA hybrid composites. Keywords: shape memory alloys, Nitinol, ABAQUS, finite element analysis, post-buckling control, shape control, deflection control, adaptive stiffening, morphing, constitutive modeling, user element

Effect of flexibility of substructures upon thermal behaviour of spherical double layer space truss domes. Part II: Gradient & partial loading

This paper presents the second part of a study on the influence of the type and properties of support conditions on the thermal behaviour of spherical double layer space truss roofs. Whereas the first part focused on the consequences of uniform thermal loadings, this paper studies the effects of support flexibilities on the behaviour of such structures subjected to gradient and partial loadings. It is observed that the thermal forces are very high and depend on the magnitude of temperature and the dome size. It is also pointed that the important point in partial loading is the unsymmetrical deformation and behaviour of the dome, while in gradient loading it is the rotational deformations. Finally, it is concluded that the use of rigid supports should be carefully examined.

Effect of flexibility of substructures upon thermal behaviour of spherical double layer space truss domes. Part I: Uniform thermal loading

Double layer space trusses are one of the most popular lightweight structures selected for covering large span roofs. These highly redundant and stiff structures, which consist of thousands of members and joints, are normally single structural assemblies, without expansion joints, and are thus required to be free to expand and contract without restraints. The type and properties of supports, which may permit or restrain radial movements of the structures, can greatly influence their behaviour. The aim of this study is to present an assessment of the influence of support flexibility on the behaviour of double layer space truss domes subjected to uniform thermal loading.